C((t))is the formal Laurent series over the field C of complex numbers.It is a henselian valued field,and its valuation ring,denoted by C[[t]],is the formal power series over C.Let K be any model of Th(C((t)))with OK ...C((t))is the formal Laurent series over the field C of complex numbers.It is a henselian valued field,and its valuation ring,denoted by C[[t]],is the formal power series over C.Let K be any model of Th(C((t)))with OK its valuation ring and k its residue field.Then k is algebraically closed and OK is elemenatry equivalent to C[[t]].We first describe the definable subsets of OK,showing that every definable subset X of OK is either res-finite or res-cofinite,i.e.,the residue res(X)of X,is either finite or cofinite in k.Moreover,X is res-finite iff OK\X is res-cofinite.Applying this result,we show that GL(n,OK),the group of invertible n by n matrices over the valuation ring,is stably dominated via the residue map.As a consequence,we conclude that GL(n,OK)is generically stable,generalizing Y.Halevi's result,where K is an algebraically closed valued field.展开更多
The invariant determinants ha Banach algebras are discussed and a necessary and sufficient condition for those integral traced unital Barach algebra(A,τ) admitting a G-invari- ant determinant is obtained,where G is a...The invariant determinants ha Banach algebras are discussed and a necessary and sufficient condition for those integral traced unital Barach algebra(A,τ) admitting a G-invari- ant determinant is obtained,where G is a group of trace preserving automorphisms of A.展开更多
Let R be a commutative ring with an identity element, G a finitely generated abelian group. In this paper,we investigate necessary and sufficient conditions on G and R such that every finitely generated projective RG ...Let R be a commutative ring with an identity element, G a finitely generated abelian group. In this paper,we investigate necessary and sufficient conditions on G and R such that every finitely generated projective RG module can be extended from R.展开更多
Let G be type B_2 and denote the two simple roots a and β with α the short one. If B is a Borel subgroup of G, X a character of B, and(X) a induced line bundle on G/B, we denote by H^1 (X)=H^1 (G/B, (X)) the first c...Let G be type B_2 and denote the two simple roots a and β with α the short one. If B is a Borel subgroup of G, X a character of B, and(X) a induced line bundle on G/B, we denote by H^1 (X)=H^1 (G/B, (X)) the first cohomology group of (X). Our main results in this paperare: Theorem Let G be type B_2;x∈X(T) be p-regular and 1≤a<p. Then H^1(X) is a simple G-module iff one of the following conditions Ⅰ)-Ⅳ> holds: Ⅰ) X∈s_α·C_0 Ⅱ) X∈s_β·C_0 Ⅲ) Ⅳ)展开更多
We prove that the adjoint semigroup of an implicative BCK algebra is an upper semilattice, and the adjoint semigroup of an implicative BCK algebra with condition(s) is a generalized Boolean algebra. Moreover we prov...We prove that the adjoint semigroup of an implicative BCK algebra is an upper semilattice, and the adjoint semigroup of an implicative BCK algebra with condition(s) is a generalized Boolean algebra. Moreover we prove the adjoint semigroup of a bounded implicative BCK algebra is a Boolean algebra.展开更多
We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the...We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author's previous works on this topic.展开更多
基金supported by The National Social Science Fund of China(Grant No.20CZX050)。
文摘C((t))is the formal Laurent series over the field C of complex numbers.It is a henselian valued field,and its valuation ring,denoted by C[[t]],is the formal power series over C.Let K be any model of Th(C((t)))with OK its valuation ring and k its residue field.Then k is algebraically closed and OK is elemenatry equivalent to C[[t]].We first describe the definable subsets of OK,showing that every definable subset X of OK is either res-finite or res-cofinite,i.e.,the residue res(X)of X,is either finite or cofinite in k.Moreover,X is res-finite iff OK\X is res-cofinite.Applying this result,we show that GL(n,OK),the group of invertible n by n matrices over the valuation ring,is stably dominated via the residue map.As a consequence,we conclude that GL(n,OK)is generically stable,generalizing Y.Halevi's result,where K is an algebraically closed valued field.
文摘A determinant theory is developed for Banach algebras and a characterization of those traced unital Banach algebras admitting a determinant is given.
文摘The invariant determinants ha Banach algebras are discussed and a necessary and sufficient condition for those integral traced unital Barach algebra(A,τ) admitting a G-invari- ant determinant is obtained,where G is a group of trace preserving automorphisms of A.
文摘Let R be a commutative ring with an identity element, G a finitely generated abelian group. In this paper,we investigate necessary and sufficient conditions on G and R such that every finitely generated projective RG module can be extended from R.
文摘Let G be type B_2 and denote the two simple roots a and β with α the short one. If B is a Borel subgroup of G, X a character of B, and(X) a induced line bundle on G/B, we denote by H^1 (X)=H^1 (G/B, (X)) the first cohomology group of (X). Our main results in this paperare: Theorem Let G be type B_2;x∈X(T) be p-regular and 1≤a<p. Then H^1(X) is a simple G-module iff one of the following conditions Ⅰ)-Ⅳ> holds: Ⅰ) X∈s_α·C_0 Ⅱ) X∈s_β·C_0 Ⅲ) Ⅳ)
文摘We prove that the adjoint semigroup of an implicative BCK algebra is an upper semilattice, and the adjoint semigroup of an implicative BCK algebra with condition(s) is a generalized Boolean algebra. Moreover we prove the adjoint semigroup of a bounded implicative BCK algebra is a Boolean algebra.
基金Supported by the National Natural Science Foundation of China(10371051)
文摘We study diagonal invariant ideals of topologically graded C*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author's previous works on this topic.
