In this paper,we introduce the notion of G_(C)-X-injective modules,where X denotes a class of left S-modules and C represents a faithfully semidualizing bimodule.Under the condition that X satisfies certain hypotheses...In this paper,we introduce the notion of G_(C)-X-injective modules,where X denotes a class of left S-modules and C represents a faithfully semidualizing bimodule.Under the condition that X satisfies certain hypotheses,some properties and some equivalent characterizations of G_(C)-X-injective modules are investigated,and we also show that the triple(■,cores■,■)is a weak co-AB-context.As an application,two complete cotorsion pairs and a new model structure in Mod S are given.展开更多
In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests mo...In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests modulo this biideal.As an application,a connected graded bialgebra and so a graded Hopf algebra on matching Rota-Baxter algebras are constructed,which simplifies the Hopf algebraic structure proposed by[Pacific J.Math.,2022,317(2):441-475].展开更多
文摘In this paper,we introduce the notion of G_(C)-X-injective modules,where X denotes a class of left S-modules and C represents a faithfully semidualizing bimodule.Under the condition that X satisfies certain hypotheses,some properties and some equivalent characterizations of G_(C)-X-injective modules are investigated,and we also show that the triple(■,cores■,■)is a weak co-AB-context.As an application,two complete cotorsion pairs and a new model structure in Mod S are given.
基金Supported by NSFC(No.12101316)Belt and Road Innovative Talents Exchange Foreign Experts project(No.DL2023014002L)。
文摘In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests modulo this biideal.As an application,a connected graded bialgebra and so a graded Hopf algebra on matching Rota-Baxter algebras are constructed,which simplifies the Hopf algebraic structure proposed by[Pacific J.Math.,2022,317(2):441-475].
