For a ring endomorphism α, in this paper we introduce the notion of s-power- serieswise nil-Armendariz rings, which are a generalization of α-power-serieswise Armendariz rings. A number of properties of this general...For a ring endomorphism α, in this paper we introduce the notion of s-power- serieswise nil-Armendariz rings, which are a generalization of α-power-serieswise Armendariz rings. A number of properties of this generalization are established, and the extensions of α- power-serieswise nil-Armendariz rings are investigated. Which generalizes the corresponding results of nil-Armendariz rings and power-serieswise nil-Armendariz rings.展开更多
In this article,we present the multiplicative Jordan decomposition in integral group ring of group K8 × C5,where K8 is the quaternion group of order 8.Thus,we give a positive answer to the question raised by Hale...In this article,we present the multiplicative Jordan decomposition in integral group ring of group K8 × C5,where K8 is the quaternion group of order 8.Thus,we give a positive answer to the question raised by Hales A W,Passi I B S and Wilson L E in the paper 'The multiplicative Jordan decomposition in group rings II.展开更多
In this paper,we prove that the special linear Lie superalgebra sl(m,n)can be generated by two nilpotent elements.In particular,the two series of sl(3,n)and sl(m,2)can be generated by one and a half nilpotent generato...In this paper,we prove that the special linear Lie superalgebra sl(m,n)can be generated by two nilpotent elements.In particular,the two series of sl(3,n)and sl(m,2)can be generated by one and a half nilpotent generators,which means that for any nonzero nilpotent element,there exists a nilpotent element such that these two elements can generate the whole Lie superalgebra.展开更多
Let F be an algebraically closed field of characteristic p 〉 3, and g be the Witt algebra over F. Let N be the nilpotent cone of g. An explicit description of N is given, so that the conjugacy classes of Borel subalg...Let F be an algebraically closed field of characteristic p 〉 3, and g be the Witt algebra over F. Let N be the nilpotent cone of g. An explicit description of N is given, so that the conjugacy classes of Borel subalgebras of g under the automorphism group of g are determined. In contrast with only one conjugacy class of Borel subalgebras in a classical simple Lie algebra, there are two conjugacy classes of Borel subalgebras in g. The representatives of conjugacy classes of Borel subalgebras, i.e.,the so-called standard Borel subalgebras, are precisely given.展开更多
文摘For a ring endomorphism α, in this paper we introduce the notion of s-power- serieswise nil-Armendariz rings, which are a generalization of α-power-serieswise Armendariz rings. A number of properties of this generalization are established, and the extensions of α- power-serieswise nil-Armendariz rings are investigated. Which generalizes the corresponding results of nil-Armendariz rings and power-serieswise nil-Armendariz rings.
文摘In this article,we present the multiplicative Jordan decomposition in integral group ring of group K8 × C5,where K8 is the quaternion group of order 8.Thus,we give a positive answer to the question raised by Hales A W,Passi I B S and Wilson L E in the paper 'The multiplicative Jordan decomposition in group rings II.
基金supported by the NNSF of China(No.12001141 and No.11971134)NSF of Heilongjiang Province(No.LH2024A014)GIF of Harbin Normal University(No.HSDSSCX2021-14).
文摘In this paper,we prove that the special linear Lie superalgebra sl(m,n)can be generated by two nilpotent elements.In particular,the two series of sl(3,n)and sl(m,2)can be generated by one and a half nilpotent generators,which means that for any nonzero nilpotent element,there exists a nilpotent element such that these two elements can generate the whole Lie superalgebra.
基金Supported by National Natural Science Foundation of China(Grant Nos.11201293 and 11271130)the Innovation Program of Shanghai Municipal Education Commission(Grant Nos.13YZ077 and 12ZZ038)
文摘Let F be an algebraically closed field of characteristic p 〉 3, and g be the Witt algebra over F. Let N be the nilpotent cone of g. An explicit description of N is given, so that the conjugacy classes of Borel subalgebras of g under the automorphism group of g are determined. In contrast with only one conjugacy class of Borel subalgebras in a classical simple Lie algebra, there are two conjugacy classes of Borel subalgebras in g. The representatives of conjugacy classes of Borel subalgebras, i.e.,the so-called standard Borel subalgebras, are precisely given.
