Let A be a basic hereditary artin algebra and R = A Q be the trivial extension of A by its minimal injective cogenerator Q. We construct some right （left） almost split morphisms and irreducible morphisms in modR thr...Let A be a basic hereditary artin algebra and R = A Q be the trivial extension of A by its minimal injective cogenerator Q. We construct some right （left） almost split morphisms and irreducible morphisms in modR through the corresponding morphisms in modA. Furthermore, we can determine its almost split sequences in modR.展开更多
Let A be a Koszul algebra, and let M be a graded A-bimodule. We prove that the trivial extension algebra of A by M is also a Koszul algebra whenever M is Koszul as a left A-module. Applications and examples are also p...Let A be a Koszul algebra, and let M be a graded A-bimodule. We prove that the trivial extension algebra of A by M is also a Koszul algebra whenever M is Koszul as a left A-module. Applications and examples are also provided.展开更多
In this paper we investigate a categorical aspect of n-trivial extension of a ring by a family of modules.Namely,we introduce the right(resp.,left)n-trivial extension of a category by a family of endofunctors.Among ot...In this paper we investigate a categorical aspect of n-trivial extension of a ring by a family of modules.Namely,we introduce the right(resp.,left)n-trivial extension of a category by a family of endofunctors.Among other results,projective,injective and flat objects of this category are characterized,and two applications are presented at the end of this paper.We characterize when an n-trivial extension ring is k-perfect and establish a result on the self-injective dimension of an n-trivial extension ring.展开更多
Some equivalent conditions for double Frobenius algebras to be strict ones are given. Then some examples of （strict or non-strict） double Frobenius algebras are presented. Finally, a sufficient and necessary conditi...Some equivalent conditions for double Frobenius algebras to be strict ones are given. Then some examples of （strict or non-strict） double Frobenius algebras are presented. Finally, a sufficient and necessary condition for the trivial extension of a double Frobenius algebra to be a （strict） double Frobenius algebra is given.展开更多
基金The NSF (11271119) of Chinathe NSF (1122002) of Beijing
文摘Let A be a basic hereditary artin algebra and R = A Q be the trivial extension of A by its minimal injective cogenerator Q. We construct some right （left） almost split morphisms and irreducible morphisms in modR through the corresponding morphisms in modA. Furthermore, we can determine its almost split sequences in modR.
基金The author is very grateful to the referees for helpful comments. He thanks Professor Yu Ye for numerous discussion and suggestions. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11471017）, Doctoral Research Foundation, and the Research Culture Foundation of Anhui Normal University （No. 2014xmpyll）.
文摘Let A be a Koszul algebra, and let M be a graded A-bimodule. We prove that the trivial extension algebra of A by M is also a Koszul algebra whenever M is Koszul as a left A-module. Applications and examples are also provided.
基金Dirar Benkhadra's research reported in this publication was supported by a scholarship from the Graduate Research Assis taut ships in Developing Countries Program of the Commission for Developing Countries of the International Mathematical UnionThe third author was partially supported by the grant MTM2014-54439-P from Ministerio de Economia y Competitividad.
文摘In this paper we investigate a categorical aspect of n-trivial extension of a ring by a family of modules.Namely,we introduce the right(resp.,left)n-trivial extension of a category by a family of endofunctors.Among other results,projective,injective and flat objects of this category are characterized,and two applications are presented at the end of this paper.We characterize when an n-trivial extension ring is k-perfect and establish a result on the self-injective dimension of an n-trivial extension ring.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 11471282）, the China Postdoctoral Science Foundation （Grant No. 2017M610316）, and the Natural Science Foundation of Jiangsu Province （Grant No. BK20170589）.
文摘Some equivalent conditions for double Frobenius algebras to be strict ones are given. Then some examples of （strict or non-strict） double Frobenius algebras are presented. Finally, a sufficient and necessary condition for the trivial extension of a double Frobenius algebra to be a （strict） double Frobenius algebra is given.
