In this paper, we give an answer to an open p roblem which was proposed in . We show that the supersemiprime radical is e qual to the near nil radical which was defined by XIE Bang_jie in .
Let R be a ring and a an automorphism of R. Amitsur proved that the Jacobson radical J（R[x]） of the polynomial ring R[x] is the polynomial ring over the nil ideal J（R[x]）∩R. Following Amitsur, it is shown that wh...Let R be a ring and a an automorphism of R. Amitsur proved that the Jacobson radical J（R[x]） of the polynomial ring R[x] is the polynomial ring over the nil ideal J（R[x]）∩R. Following Amitsur, it is shown that when R is an Armendaxiz ring of skew inverse Laurent series type and S is any one of the ring extensions R[x; α], R[x,x^-1;α], R[[x^-1;α]] and R（（x^-1; α））, then （S） = （R）S = Nil（S）, （S） ∩ R = Nil（R）, where is a radical in a class of radicals which includes the Wedderburn, lower nil, Levitzky and upper nil radicals.展开更多
In this paper,we introduce the notion of an almost Armendariz ring,which is a generalization of an Armendariz ring,and discuss some of its properties.It has been found that every almost Armendariz ring is weak Armenda...In this paper,we introduce the notion of an almost Armendariz ring,which is a generalization of an Armendariz ring,and discuss some of its properties.It has been found that every almost Armendariz ring is weak Armendariz but the converse is not true.We prove that a ring R is almost Armendariz if and only if R[x]is almost Armendariz.It is also shown th at if R/I is an almost Armendariz ring and I is a semicommutative ideal,then H is an almost Armendariz ring.Moreover,the class of minimal non-commutative almost Armendariz rings is completely determined,up to isomorphism(minimal means having smallest cardinality).展开更多
The noncommutative Singer-Wermer conjecture states that every linear （possibly unbounded） derivation on a （possibly noncommutative） Banach algebra maps into its Jacobson radical. This conjecture is still an open q...The noncommutative Singer-Wermer conjecture states that every linear （possibly unbounded） derivation on a （possibly noncommutative） Banach algebra maps into its Jacobson radical. This conjecture is still an open question for more than thirty years. In this paper we approach this question via linear left θ-derivations.展开更多
文摘In this paper, we give an answer to an open p roblem which was proposed in . We show that the supersemiprime radical is e qual to the near nil radical which was defined by XIE Bang_jie in .
文摘Let R be a ring and a an automorphism of R. Amitsur proved that the Jacobson radical J（R[x]） of the polynomial ring R[x] is the polynomial ring over the nil ideal J（R[x]）∩R. Following Amitsur, it is shown that when R is an Armendaxiz ring of skew inverse Laurent series type and S is any one of the ring extensions R[x; α], R[x,x^-1;α], R[[x^-1;α]] and R（（x^-1; α））, then （S） = （R）S = Nil（S）, （S） ∩ R = Nil（R）, where is a radical in a class of radicals which includes the Wedderburn, lower nil, Levitzky and upper nil radicals.
文摘In this paper,we introduce the notion of an almost Armendariz ring,which is a generalization of an Armendariz ring,and discuss some of its properties.It has been found that every almost Armendariz ring is weak Armendariz but the converse is not true.We prove that a ring R is almost Armendariz if and only if R[x]is almost Armendariz.It is also shown th at if R/I is an almost Armendariz ring and I is a semicommutative ideal,then H is an almost Armendariz ring.Moreover,the class of minimal non-commutative almost Armendariz rings is completely determined,up to isomorphism(minimal means having smallest cardinality).
文摘The noncommutative Singer-Wermer conjecture states that every linear （possibly unbounded） derivation on a （possibly noncommutative） Banach algebra maps into its Jacobson radical. This conjecture is still an open question for more than thirty years. In this paper we approach this question via linear left θ-derivations.
