In this paper we continue the study of various ring theoretic properties of Morita contexts.Necessary and sufficient conditions are obtained for a general Morita context or a trivial Morita context or a formal triangu...In this paper we continue the study of various ring theoretic properties of Morita contexts.Necessary and sufficient conditions are obtained for a general Morita context or a trivial Morita context or a formal triangular matrix ring to satisfy a certain ring property which is among being Kasch,completely primary,quasi-duo,2-primal,NI,semiprimitive,projective-free,etc.We also characterize when a general Morita context is weakly principally quasi-Baer or strongly right mininjective.展开更多
In this article,we extend the Zassenhaus lemma(also called the butterfly lemma)and the Schreier refinement theorem to the case of gyrogroups.In addition,we use these results to prove the Jordan–Hölder theorem fo...In this article,we extend the Zassenhaus lemma(also called the butterfly lemma)and the Schreier refinement theorem to the case of gyrogroups.In addition,we use these results to prove the Jordan–Hölder theorem for gyrogroups as well as some theorems regarding subgyrogroup lattices.展开更多
We introduce the notions of a four-angle Hopf quasimodule and an adjoint quasiaction over a Hopf quasigroup H in a,symmetric monoidal category C.li H possesses an adjoint quasiaction,we show that symmetric Yetter-Drin...We introduce the notions of a four-angle Hopf quasimodule and an adjoint quasiaction over a Hopf quasigroup H in a,symmetric monoidal category C.li H possesses an adjoint quasiaction,we show that symmetric Yetter-Drinfeld categories are trivial,and hence we obtain a braided monoidal category equivalence between the category of right Yetter-Drinfeld modules over H and the category of four-angle Hopf modules over H under some suitable conditions.展开更多
文摘In this paper we continue the study of various ring theoretic properties of Morita contexts.Necessary and sufficient conditions are obtained for a general Morita context or a trivial Morita context or a formal triangular matrix ring to satisfy a certain ring property which is among being Kasch,completely primary,quasi-duo,2-primal,NI,semiprimitive,projective-free,etc.We also characterize when a general Morita context is weakly principally quasi-Baer or strongly right mininjective.
文摘In this article,we extend the Zassenhaus lemma(also called the butterfly lemma)and the Schreier refinement theorem to the case of gyrogroups.In addition,we use these results to prove the Jordan–Hölder theorem for gyrogroups as well as some theorems regarding subgyrogroup lattices.
基金supported by the National Natural Science Foundation of China(Grant No.11871144)the NNSF of Jiangsu Province(No.BK20171348)the Scientific Research Foundation of Nanjing Institute of Technology(No.YKJ202040).
文摘We introduce the notions of a four-angle Hopf quasimodule and an adjoint quasiaction over a Hopf quasigroup H in a,symmetric monoidal category C.li H possesses an adjoint quasiaction,we show that symmetric Yetter-Drinfeld categories are trivial,and hence we obtain a braided monoidal category equivalence between the category of right Yetter-Drinfeld modules over H and the category of four-angle Hopf modules over H under some suitable conditions.
