The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- reg...The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- regular general rings are provided. It is shown that I is strongly π-regular if and only if, for each x ∈I, x^n =x^n＋1y = zx^n＋1 for n ≥ 1 and y, z ∈ I if and only if every element of I is strongly π-regular. It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.展开更多
Let T(R) be a two-order upper matrix algebra over the semilocal ring R which is determined by R=F×F where F is a field such that CharF=0. In this paper, we prove that any Jordan automorphism of T(R) can be decomp...Let T(R) be a two-order upper matrix algebra over the semilocal ring R which is determined by R=F×F where F is a field such that CharF=0. In this paper, we prove that any Jordan automorphism of T(R) can be decomposed into a product of involutive, inner and diagonal automorphisms.展开更多
The upper triangular matrix of Lie algebra is used to construct integrable couplings of discrete solition equations. Correspondingly, a feasible way to construct integrable couplings is presented. A nonlinear lattice ...The upper triangular matrix of Lie algebra is used to construct integrable couplings of discrete solition equations. Correspondingly, a feasible way to construct integrable couplings is presented. A nonlinear lattice soliton equation spectral problem is obtained and leads to a novel hierarchy of the nonlinear lattice equation hierarchy. It indicates that the study of integrable couplings using upper triangular matrix of Lie algebra is an important step towards constructing integrable systems.展开更多
Let R be a commutative ring with identity, Nn(R) the matrix algebra consisting of all n × n strictly upper triangular matrices over R with the usual product operation. An R-linear map φ : Nn(R) → Nn(R) is said ...Let R be a commutative ring with identity, Nn(R) the matrix algebra consisting of all n × n strictly upper triangular matrices over R with the usual product operation. An R-linear map φ : Nn(R) → Nn(R) is said to be an SZ-derivation of Nn(R) if x2 = 0 implies that φ(x)x+xφ(x) = 0. It is said to be an S-derivation of Nn(R) if φ(x2) = φ(x)x+xφ(x) for any x ∈ Nn(R). It is said to be a PZ-derivation of Nn(R) if xy = 0 implies that φ(x)y+xφ(y) = 0. In this paper, by constructing several types of standard SZ-derivations of Nn(R), we first characterize all SZ-derivations of Nn(R). Then, as its application, we determine all S-derivations and PZ- derivations of Nn(R), respectively.展开更多
基金The Foundation for Excellent Doctoral Dissertationof Southeast University (NoYBJJ0507)the National Natural ScienceFoundation of China (No10571026)the Natural Science Foundation ofJiangsu Province (NoBK2005207)
文摘The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- regular general rings are provided. It is shown that I is strongly π-regular if and only if, for each x ∈I, x^n =x^n＋1y = zx^n＋1 for n ≥ 1 and y, z ∈ I if and only if every element of I is strongly π-regular. It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.
文摘Let T(R) be a two-order upper matrix algebra over the semilocal ring R which is determined by R=F×F where F is a field such that CharF=0. In this paper, we prove that any Jordan automorphism of T(R) can be decomposed into a product of involutive, inner and diagonal automorphisms.
基金＊The project supported by the National Key Basic Research Development of China under Grant No. N1998030600 and National Natural Science Foundation of China under Grant No. 10072013
文摘The upper triangular matrix of Lie algebra is used to construct integrable couplings of discrete solition equations. Correspondingly, a feasible way to construct integrable couplings is presented. A nonlinear lattice soliton equation spectral problem is obtained and leads to a novel hierarchy of the nonlinear lattice equation hierarchy. It indicates that the study of integrable couplings using upper triangular matrix of Lie algebra is an important step towards constructing integrable systems.
基金Fond of China University of Mining and Technology
文摘Let R be a commutative ring with identity, Nn(R) the matrix algebra consisting of all n × n strictly upper triangular matrices over R with the usual product operation. An R-linear map φ : Nn(R) → Nn(R) is said to be an SZ-derivation of Nn(R) if x2 = 0 implies that φ(x)x+xφ(x) = 0. It is said to be an S-derivation of Nn(R) if φ(x2) = φ(x)x+xφ(x) for any x ∈ Nn(R). It is said to be a PZ-derivation of Nn(R) if xy = 0 implies that φ(x)y+xφ(y) = 0. In this paper, by constructing several types of standard SZ-derivations of Nn(R), we first characterize all SZ-derivations of Nn(R). Then, as its application, we determine all S-derivations and PZ- derivations of Nn(R), respectively.
