Let K be a finite abelian group and let H be the holomorph of K. It is shown that every Coleman automorphism of H is an inner automorphism. As an immediate consequence of this result, it is obtained that the normalize...Let K be a finite abelian group and let H be the holomorph of K. It is shown that every Coleman automorphism of H is an inner automorphism. As an immediate consequence of this result, it is obtained that the normalizer property holds for H.展开更多
Let H2 be Sweedler＇s 4-dimensional Hopf algebra and r（H2） be the corresponding Green ring of H2. In this paper, we investigate the automorphism groups of Green ring r（H2） and Green algebra F（H2） = r（H2） zF, ...Let H2 be Sweedler＇s 4-dimensional Hopf algebra and r（H2） be the corresponding Green ring of H2. In this paper, we investigate the automorphism groups of Green ring r（H2） and Green algebra F（H2） = r（H2） zF, where F is a field, whose characteristics is not equal to 2. We prove that the automorphism group of r（H2） is isomorphic to K4, where K4 is the Klein group, and the automorphism group of F（H2） is the semidirect product of Z2 and G, where G = F ／ {1/2} with multiplication given by a. b = 1 - a - b ＋ 2ab.展开更多
Let R be a prime ring with center Z, 5 ： R → R a nonzero skew derivation, and n a fixed positive integer. In this paper, we show that R is a commutative ring if （i） [（δ（[x, y]）, [x, y]]n = 0 for all x, y ∈ R ...Let R be a prime ring with center Z, 5 ： R → R a nonzero skew derivation, and n a fixed positive integer. In this paper, we show that R is a commutative ring if （i） [（δ（[x, y]）, [x, y]]n = 0 for all x, y ∈ R or （ii） [（δ（x）, x]n e Z for all x ∈ R, except some specific cases.展开更多
Let R be a commutative ring containing 1, T（R） is a non-Abelian group defined by the following.Generators: x<sub>ij</sub>（a）, i【j, i, j=1, 2,…, n, a∈R.
Let R be a prime ring, L a noncentral Lie ideal and a nontrivialautomorphism of R such that us（u）ut = 0 for all u 2 L, where s; t are fixednon-negative integers. If either charR 〉 s ＋ t or charR = 0, then R satis...Let R be a prime ring, L a noncentral Lie ideal and a nontrivialautomorphism of R such that us（u）ut = 0 for all u 2 L, where s; t are fixednon-negative integers. If either charR 〉 s ＋ t or charR = 0, then R satisfies s4, thestandard identity in four variables. We also examine the identity （σ（[x; y]）-[x; y]）n =0 for all x; y ∈ I, where I is a nonzero ideal of R and n is a fixed positive integer. Ifeither charR 〉 n or charR = 0, then R is commutative.展开更多
Let R be a prime ring with an automorphism σ≠1, an identity map. Let L be a noncentral Lie ideal of R such that \xσ, x] ∈Z for all x ∈ L, where Z is the center of R. Then L is contained in the center of R, unless...Let R be a prime ring with an automorphism σ≠1, an identity map. Let L be a noncentral Lie ideal of R such that \xσ, x] ∈Z for all x ∈ L, where Z is the center of R. Then L is contained in the center of R, unless char(R) = 2 and dimcRC = 4.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11171169)the Doctoral Fund of Shandong Province(Grant No.BS2012SF003)+1 种基金a Project of Shandong Province Higher Educational Science and Technology Program(Grant No.J14LI10)a Project of Shandong Province Higher Educational Excellent Backbone Teachers for International Cooperation and Training
文摘Let K be a finite abelian group and let H be the holomorph of K. It is shown that every Coleman automorphism of H is an inner automorphism. As an immediate consequence of this result, it is obtained that the normalizer property holds for H.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 11471282）.
文摘Let H2 be Sweedler＇s 4-dimensional Hopf algebra and r（H2） be the corresponding Green ring of H2. In this paper, we investigate the automorphism groups of Green ring r（H2） and Green algebra F（H2） = r（H2） zF, where F is a field, whose characteristics is not equal to 2. We prove that the automorphism group of r（H2） is isomorphic to K4, where K4 is the Klein group, and the automorphism group of F（H2） is the semidirect product of Z2 and G, where G = F ／ {1/2} with multiplication given by a. b = 1 - a - b ＋ 2ab.
文摘Let R be a prime ring with center Z, 5 ： R → R a nonzero skew derivation, and n a fixed positive integer. In this paper, we show that R is a commutative ring if （i） [（δ（[x, y]）, [x, y]]n = 0 for all x, y ∈ R or （ii） [（δ（x）, x]n e Z for all x ∈ R, except some specific cases.
文摘Let R be a commutative ring containing 1, T（R） is a non-Abelian group defined by the following.Generators: x<sub>ij</sub>（a）, i【j, i, j=1, 2,…, n, a∈R.
基金The NSF(1408085QA08) of Anhui Provincethe Natural Science Research Foundation(KJ2014A183) of Anhui Provincial Education DepartmentAnhui Province College Excellent Young Talents Fund Project(2012SQRL155) of China
文摘Let R be a prime ring, L a noncentral Lie ideal and a nontrivialautomorphism of R such that us（u）ut = 0 for all u 2 L, where s; t are fixednon-negative integers. If either charR 〉 s ＋ t or charR = 0, then R satisfies s4, thestandard identity in four variables. We also examine the identity （σ（[x; y]）-[x; y]）n =0 for all x; y ∈ I, where I is a nonzero ideal of R and n is a fixed positive integer. Ifeither charR 〉 n or charR = 0, then R is commutative.
文摘Let R be a prime ring with an automorphism σ≠1, an identity map. Let L be a noncentral Lie ideal of R such that \xσ, x] ∈Z for all x ∈ L, where Z is the center of R. Then L is contained in the center of R, unless char(R) = 2 and dimcRC = 4.
