In this paper,we discuss the related properties of some particular derivations in semihoops and give some characterizations of them.Then,we prove that every Heyting algebra is isomorphic to the algebra of all multipli...In this paper,we discuss the related properties of some particular derivations in semihoops and give some characterizations of them.Then,we prove that every Heyting algebra is isomorphic to the algebra of all multiplicative derivations and show that every Boolean algebra is isomorphic to the algebra of all implicative derivations.Finally,we show that the sets of multiplicative and implicative derivations on bounded regular idempotent semihoops are in oneto-one correspondence.展开更多
We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provid...We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provide all generalized derivations for complex low-dimensional dendriform algebras.展开更多
Let P be a parabolic subalgebra of a general linear Lie algebra gl（n,F） over a field F, where n ≥ 3, F contains at least n different elements, and char（F） ≠ 2. In this article, we prove that generalized derivati...Let P be a parabolic subalgebra of a general linear Lie algebra gl（n,F） over a field F, where n ≥ 3, F contains at least n different elements, and char（F） ≠ 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation.展开更多
In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations an...In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic.In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive(implicative)derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97-113] and [Information Sciences, 178(2008),307-316].展开更多
A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-L...A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.展开更多
Let A be a unital algebra and M be a unital .A-bimodule. A linear map δ ： A →M is said to be Jordan derivable at a nontrivial idempotent P ∈A if δ（A） o B ＋ A o δ（B） =δ（A o B） for any A,B ∈ .4 with A o B...Let A be a unital algebra and M be a unital .A-bimodule. A linear map δ ： A →M is said to be Jordan derivable at a nontrivial idempotent P ∈A if δ（A） o B ＋ A o δ（B） =δ（A o B） for any A,B ∈ .4 with A o B = P, here A o B = AB ＋ BA is the usual Jordan product. In this article, we show that if ,A = AlgAN is a Hilbert space nest Mgebra and M = B（H）, or A =M= B（X）, then, a linear mapδ： A→M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P∈ B（X） if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained.展开更多
In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some ...In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.展开更多
In this paper, we prove that any nonlinear Jordan higher derivation on triangular algebras is an additive higher derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algebras over infinit...In this paper, we prove that any nonlinear Jordan higher derivation on triangular algebras is an additive higher derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algebras over infinite dimensional Hilbert suaces is inner.展开更多
In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen...In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf（x＋y/r）＋sg（x-y/s）=2h（x）for r, s ∈ R ／ {0} on Hilbert C＊-modules, where f, g, and h are mappings from a Hilbert C＊-module M to M.展开更多
By using properties of triangular algebra, we prove that if derivations D and G on a triangular algebra T satisfy certain generalized identities, then both D and G are zero mappings. As a corollary we get that if D an...By using properties of triangular algebra, we prove that if derivations D and G on a triangular algebra T satisfy certain generalized identities, then both D and G are zero mappings. As a corollary we get that if D and G are cocentralizing on T, then both D and G are zero mappings.展开更多
In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to inv...In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to investigate isomorphisms between C＊-algebras, Lie C＊-algebras and JC＊-algebras, and derivations on C＊-algebras, Lie C＊-algebras and JC＊-algebras, associated with the Cauchy-Jensen functional equation 2f （x ＋ y/2 ＋ z ＋ w） = f（x） ＋ f（y） ＋ 2f（z） ＋ 2f（w）.展开更多
In this paper we discuss the linear combination of derivations in prime rings which was initiated by Niu Fengwen. Our aim is to improve Niu's result. For the proof of the main theorem we generalize a result of Bre...In this paper we discuss the linear combination of derivations in prime rings which was initiated by Niu Fengwen. Our aim is to improve Niu's result. For the proof of the main theorem we generalize a result of Bresar and obtain a lemma that is of independent interest.展开更多
Let gl0|2 be a subalgebra of the general linear Lie superalgebra.In this paper,outer derivations from gl0|2 to the generalized Witt Lie superalgebra are completely determined by matrices.
This article gives characterizations of generalized derivations with skew nilpotent values on noncommutative Lie ideals of a prime ring. The results simultaneously generalize the ones of Herstein, Lee and Carini et al.
Let N be a nest on a Banach space X, and Alg N be the associated nest algebra. It is shown that if there exists a non-trivial element in N which is complemented in X, then D = （Ln）n∈N is a Lie higher derivation of ...Let N be a nest on a Banach space X, and Alg N be the associated nest algebra. It is shown that if there exists a non-trivial element in N which is complemented in X, then D = （Ln）n∈N is a Lie higher derivation of AlgAl if and only if each Ln has the form Ln（A） ： Tn（A） ＋ hn（A）I for all A ∈ AlgN, where （Tn）n∈N is a higher derivation and （hn）n∈N is a sequence of additive functionals satisfying hn（[A,B]） = 0 for all A,B ∈ AlgN and all n ∈ N.展开更多
Let R be a prime ring with center Z and S包含 R. Two mappings D and G of R into itself are called cocentralizing on S if D（x）x - xG（x） ∈ Z for all x ∈S. The main purpose of this paper is to describe the structur...Let R be a prime ring with center Z and S包含 R. Two mappings D and G of R into itself are called cocentralizing on S if D（x）x - xG（x） ∈ Z for all x ∈S. The main purpose of this paper is to describe the structure of generalized derivations which are cocentralizing on ideals, left ideals and Lie ideals of a prime ring, respectively. The semiprime ease is also considered.展开更多
In this paper, it is proved that under certain conditions, each Jordan left derivation on a generalized matrix algebra is zero and each generalized Jordan left derivation is a generalized left derivation.
In this paper, it is proved that a monomial derivation d of k[x, y, z] has no Darboux polynomials if and only if d is a strict derivation with a trivial ring of constants, and we give the specific conditions when it h...In this paper, it is proved that a monomial derivation d of k[x, y, z] has no Darboux polynomials if and only if d is a strict derivation with a trivial ring of constants, and we give the specific conditions when it has no Darboux polynomials.展开更多
基金Supported by the National Natural Science Foundation of China(12271319).
文摘In this paper,we discuss the related properties of some particular derivations in semihoops and give some characterizations of them.Then,we prove that every Heyting algebra is isomorphic to the algebra of all multiplicative derivations and show that every Boolean algebra is isomorphic to the algebra of all implicative derivations.Finally,we show that the sets of multiplicative and implicative derivations on bounded regular idempotent semihoops are in oneto-one correspondence.
文摘We introduce and investigate the properties of a generalization of the derivation of dendriform algebras. We specify all possible parameter values for the generalized derivations, which depend on parameters. We provide all generalized derivations for complex low-dimensional dendriform algebras.
基金supported by the National Natural Science Foundation of China(11101084,11071040)the Fujian Province Nature Science Foundation of China(2013J01005)
文摘Let P be a parabolic subalgebra of a general linear Lie algebra gl（n,F） over a field F, where n ≥ 3, F contains at least n different elements, and char（F） ≠ 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation.
基金Supported by a grant of National Natural Science Foundation of China(12001243,61976244,12171294,11961016)the Natural Science Basic Research Plan in Shaanxi Province of China(2020JQ-762,2021JQ-580)。
文摘In this paper, we review some of their related properties of derivations on MValgebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic.In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive(implicative)derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97-113] and [Information Sciences, 178(2008),307-316].
基金Supported by the National Natural Science Foundation of China(11501523,61673320)。
文摘A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.
基金Supported by National Natural Foundation of China(11001194)Provincial International Cooperation Project of Shanxi(2014081027-2)
文摘Let A be a unital algebra and M be a unital .A-bimodule. A linear map δ ： A →M is said to be Jordan derivable at a nontrivial idempotent P ∈A if δ（A） o B ＋ A o δ（B） =δ（A o B） for any A,B ∈ .4 with A o B = P, here A o B = AB ＋ BA is the usual Jordan product. In this article, we show that if ,A = AlgAN is a Hilbert space nest Mgebra and M = B（H）, or A =M= B（X）, then, a linear mapδ： A→M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P∈ B（X） if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained.
基金National Natural Science Foundation of China(10271076)
文摘In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.
文摘In this paper, we prove that any nonlinear Jordan higher derivation on triangular algebras is an additive higher derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algebras over infinite dimensional Hilbert suaces is inner.
文摘In this article, we introduce the notion of generalized derivations on Hilbert C＊-modules. We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized Cauchy-Jensen type functional equationrf（x＋y/r）＋sg（x-y/s）=2h（x）for r, s ∈ R ／ {0} on Hilbert C＊-modules, where f, g, and h are mappings from a Hilbert C＊-module M to M.
基金The NSF(11101175,11371165) of China985 Project211 Project
文摘By using properties of triangular algebra, we prove that if derivations D and G on a triangular algebra T satisfy certain generalized identities, then both D and G are zero mappings. As a corollary we get that if D and G are cocentralizing on T, then both D and G are zero mappings.
基金supported by the Daejin University grants in 2010
文摘In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to investigate isomorphisms between C＊-algebras, Lie C＊-algebras and JC＊-algebras, and derivations on C＊-algebras, Lie C＊-algebras and JC＊-algebras, associated with the Cauchy-Jensen functional equation 2f （x ＋ y/2 ＋ z ＋ w） = f（x） ＋ f（y） ＋ 2f（z） ＋ 2f（w）.
文摘In this paper we discuss the linear combination of derivations in prime rings which was initiated by Niu Fengwen. Our aim is to improve Niu's result. For the proof of the main theorem we generalize a result of Bresar and obtain a lemma that is of independent interest.
基金the Fundamental Research Fund(2572018BC15)for the Central Universitiesthe NSF(11171055)of China
文摘Let gl0|2 be a subalgebra of the general linear Lie superalgebra.In this paper,outer derivations from gl0|2 to the generalized Witt Lie superalgebra are completely determined by matrices.
文摘This article gives characterizations of generalized derivations with skew nilpotent values on noncommutative Lie ideals of a prime ring. The results simultaneously generalize the ones of Herstein, Lee and Carini et al.
基金supported by NSF (10771157) of ChinaResearch Fund (2007-38) of Shanxi for Returned ScholarsFoundation of Shanxi University
文摘Let N be a nest on a Banach space X, and Alg N be the associated nest algebra. It is shown that if there exists a non-trivial element in N which is complemented in X, then D = （Ln）n∈N is a Lie higher derivation of AlgAl if and only if each Ln has the form Ln（A） ： Tn（A） ＋ hn（A）I for all A ∈ AlgN, where （Tn）n∈N is a higher derivation and （hn）n∈N is a sequence of additive functionals satisfying hn（[A,B]） = 0 for all A,B ∈ AlgN and all n ∈ N.
文摘Let R be a prime ring with center Z and S包含 R. Two mappings D and G of R into itself are called cocentralizing on S if D（x）x - xG（x） ∈ Z for all x ∈S. The main purpose of this paper is to describe the structure of generalized derivations which are cocentralizing on ideals, left ideals and Lie ideals of a prime ring, respectively. The semiprime ease is also considered.
基金Fundamental Research Funds (N110423007) for the Central Universities
文摘In this paper, it is proved that under certain conditions, each Jordan left derivation on a generalized matrix algebra is zero and each generalized Jordan left derivation is a generalized left derivation.
基金The NSF(11526104)of Chinathe Youth Research Funds(LDGY2015001)from Liaoning University
文摘In this paper, it is proved that a monomial derivation d of k[x, y, z] has no Darboux polynomials if and only if d is a strict derivation with a trivial ring of constants, and we give the specific conditions when it has no Darboux polynomials.
