In this article,we introduce and study the class of approximately Artinian(Noetherian)C^(*)-algebras,called AR-algebras(AN-algebras),which is a simultaneous generalization of Artinian(Noetherian)C*-algebras and AF-alg...In this article,we introduce and study the class of approximately Artinian(Noetherian)C^(*)-algebras,called AR-algebras(AN-algebras),which is a simultaneous generalization of Artinian(Noetherian)C*-algebras and AF-algebras.We study properties such as the ideal property and topological dimension zero for them.In particular,we show that a faithful AR or AN algebra is strongly purely infinite iff it is purely infinite iff it is weakly purely infinite.This extends the Kirchberg's O_(∞)-absorption theorem,and implies that a weakly purely infinite C^(*)-algebra is Noetherian iff every its ideal has a full projection.展开更多
The purpose to this paper is to study the existence problem of solutions to the vector quasivariational inequality for vector-valued functions inH-space.
Left (right) C-semigroups are the regular semigroups satisfying the following condition:eSSe (SeeS) for every e∈E (the set of idempotents of S). Refs. [1, 2] give the left(right) semi-spined product structure and the...Left (right) C-semigroups are the regular semigroups satisfying the following condition:eSSe (SeeS) for every e∈E (the set of idempotents of S). Refs. [1, 2] give the left(right) semi-spined product structure and the left (right) △-product structure of a left(right) C-semigroup, respectively. It is easy to see that the above condition defining a reg-ular semigroup S to be a left (right) C-semigroup may be replaced by the following condi-tion:展开更多
In this paper,we first generalize Yang and Ju’s(J Glob Optim 65:563–573,2016)result in Hausdorff topological vector spaces.Second,we introduce the model of leader-follower games with infinitely many leaders and foll...In this paper,we first generalize Yang and Ju’s(J Glob Optim 65:563–573,2016)result in Hausdorff topological vector spaces.Second,we introduce the model of leader-follower games with infinitely many leaders and followers,that is,infiniteleader-infinite-follower game.We next introduce the notion of weakly cooperative equilibria for infinite-leader-infinite-follower games and prove the existence result.展开更多
The object of this article is to initiate the study of a class of rings in which the right duo property is applied in relation to powers of elements and the monoid of all regular elements.Such rings shall be called ri...The object of this article is to initiate the study of a class of rings in which the right duo property is applied in relation to powers of elements and the monoid of all regular elements.Such rings shall be called right exp-DR.We investigate the structures of group rings,right quotient rings,matrix rings and(skew)polynomial rings,through the study of right exp-DR rings.In addition,we provide a method of constructing finite non-abelian p-groups for any prime p.展开更多
基金supported by grants from INSF(98029498,99013953)partly supported by a grant from IPM(96430215)。
文摘In this article,we introduce and study the class of approximately Artinian(Noetherian)C^(*)-algebras,called AR-algebras(AN-algebras),which is a simultaneous generalization of Artinian(Noetherian)C*-algebras and AF-algebras.We study properties such as the ideal property and topological dimension zero for them.In particular,we show that a faithful AR or AN algebra is strongly purely infinite iff it is purely infinite iff it is weakly purely infinite.This extends the Kirchberg's O_(∞)-absorption theorem,and implies that a weakly purely infinite C^(*)-algebra is Noetherian iff every its ideal has a full projection.
基金Supported by the Science Research Foundation of Xianning Teacher's College( No.K9911)
文摘The purpose to this paper is to study the existence problem of solutions to the vector quasivariational inequality for vector-valued functions inH-space.
基金Project supported by the National Natural Science Foundation of China.
文摘Left (right) C-semigroups are the regular semigroups satisfying the following condition:eSSe (SeeS) for every e∈E (the set of idempotents of S). Refs. [1, 2] give the left(right) semi-spined product structure and the left (right) △-product structure of a left(right) C-semigroup, respectively. It is easy to see that the above condition defining a reg-ular semigroup S to be a left (right) C-semigroup may be replaced by the following condi-tion:
基金This research was supported by the National Natural Science Foundation of China(No.11501349)Graduate Innovation Foundation sponsored by Shanghai University of Finance and Economics(No.CXJJ-2017-375).
文摘In this paper,we first generalize Yang and Ju’s(J Glob Optim 65:563–573,2016)result in Hausdorff topological vector spaces.Second,we introduce the model of leader-follower games with infinitely many leaders and followers,that is,infiniteleader-infinite-follower game.We next introduce the notion of weakly cooperative equilibria for infinite-leader-infinite-follower games and prove the existence result.
文摘The object of this article is to initiate the study of a class of rings in which the right duo property is applied in relation to powers of elements and the monoid of all regular elements.Such rings shall be called right exp-DR.We investigate the structures of group rings,right quotient rings,matrix rings and(skew)polynomial rings,through the study of right exp-DR rings.In addition,we provide a method of constructing finite non-abelian p-groups for any prime p.
