The additive （generalized） ξ-Lie derivations on prime algebras are characterized. It is shown, under some suitable assumptions, that an additive map L is an additive generalized Lie derivation if and only if it is ...The additive （generalized） ξ-Lie derivations on prime algebras are characterized. It is shown, under some suitable assumptions, that an additive map L is an additive generalized Lie derivation if and only if it is the sum of an additive generalized derivation and an additive map from the algebra into its center vanishing all commutators; is an additive （generalized） E-Lie derivation with ξ -if and only if it is an additive （generalized） derivation satisfying L（ξA） =- ξL（A） for all A. These results are then used to characterize additive （generalized） ξ-Lie derivations on several operator Mgebras such as Banach space standard operator algebras and yon Neumman algebras.展开更多
In this paper,the topological space(PF_(MP)(X),T) based on prime MP-filters of a lattice FI-algebra X is constructed firstly and we proved that it is a compact T_0-space if X with condition(P).Secondly,we restricted T...In this paper,the topological space(PF_(MP)(X),T) based on prime MP-filters of a lattice FI-algebra X is constructed firstly and we proved that it is a compact T_0-space if X with condition(P).Secondly,we restricted T to the set of all maximal MP-filters MF_(MP)(X) of X and concluded that(PF_(MP)(X),T |_(PF_(MP)(X)) )is a compact T_2 space if X with conditions(P) and(S).展开更多
We show that each irreducible, transitive finite-dimensional graded Lie algebra over a field of prime characteristic p contains an initial subalgebra in which the pth power of the adjoint transformation associated wit...We show that each irreducible, transitive finite-dimensional graded Lie algebra over a field of prime characteristic p contains an initial subalgebra in which the pth power of the adjoint transformation associated with any element in the lowest gradation space is zero.展开更多
The notion of e-filters is introduced in an MS-algebra and characterized. The concept of D-filters is introduced and a set of equivalent conditions under which every D-filter is an e-filter are given. The properties o...The notion of e-filters is introduced in an MS-algebra and characterized. The concept of D-filters is introduced and a set of equivalent conditions under which every D-filter is an e-filter are given. The properties of the space of all prime e-filters of an MS-algebra are observed. The concept of D-prime filters is introduced and then a set of equivalent conditions axe derived for a prime e-filter to become a D-prime filter in topological terms.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11101250)Youth Foundation of Shanxi Province(Grant No.2012021004)+3 种基金 Young Talents Plan for Shanxi Universitysupported by National Natural Science Foundation of China(Grant No.11171249)Research Fund for the Doctoral Program of Higher Education of China(Grant No.20101402110012)International Cooperation Program in Sciences and Technology of Shanxi Province(Grant No.2011081039)
文摘The additive （generalized） ξ-Lie derivations on prime algebras are characterized. It is shown, under some suitable assumptions, that an additive map L is an additive generalized Lie derivation if and only if it is the sum of an additive generalized derivation and an additive map from the algebra into its center vanishing all commutators; is an additive （generalized） E-Lie derivation with ξ -if and only if it is an additive （generalized） derivation satisfying L（ξA） =- ξL（A） for all A. These results are then used to characterize additive （generalized） ξ-Lie derivations on several operator Mgebras such as Banach space standard operator algebras and yon Neumman algebras.
基金Supported by the NSF of China(10371106,60774073)
文摘In this paper,the topological space(PF_(MP)(X),T) based on prime MP-filters of a lattice FI-algebra X is constructed firstly and we proved that it is a compact T_0-space if X with condition(P).Secondly,we restricted T to the set of all maximal MP-filters MF_(MP)(X) of X and concluded that(PF_(MP)(X),T |_(PF_(MP)(X)) )is a compact T_2 space if X with conditions(P) and(S).
文摘We show that each irreducible, transitive finite-dimensional graded Lie algebra over a field of prime characteristic p contains an initial subalgebra in which the pth power of the adjoint transformation associated with any element in the lowest gradation space is zero.
文摘The notion of e-filters is introduced in an MS-algebra and characterized. The concept of D-filters is introduced and a set of equivalent conditions under which every D-filter is an e-filter are given. The properties of the space of all prime e-filters of an MS-algebra are observed. The concept of D-prime filters is introduced and then a set of equivalent conditions axe derived for a prime e-filter to become a D-prime filter in topological terms.
