Let R be a commutative ring with unity and let M, N be unitary R-modules. In this research, we give generalizations for the concepts: weakly relative injectivity, relative tightness and weakly injectivity of modules. We call M weakly N-quasi-injective, if for each f  Hom(N,ï) there exists a submodule X of ï such that f (N) ïƒ X ≈ M, where ï is the quasi-injective hull of M. And we call M N-quasi-tight, if every quotient N / K of N which embeds in ï embeds in M. While we call M weakly quasi-injective if M is weakly N-quasiinjective for every finitely generated R-module N. Moreover, we generalize some properties of weakly N-injective, N-tight and weakly injective modules to weakly N-quasi-injective, N-quasi-tight and weakly quasi-injective modules respectively. The relations among these concepts are also studied.
Some authors studied modules with annihilator of every nonzero submodule is prime, primary or maximal. In this paper, we introduce and study annsemimaximal and coannsemimaximal modules, where an R-module M is called annsemimaximal (resp. coannsemimaximal) if annRN (resp. ) is semimaximal ideal of R for each nonzero submodule N of M.
An -module is extending if every submodule of is essential in a direct summand of . Following Clark, an -module is purely extending if every submodule of is essential in a pure submodule of . It is clear purely extending is generalization of extending modules. Following Birkenmeier and Tercan, an -module is Goldie extending if, for each submodule of , there is a direct summand D of such that . In this paper, we introduce and study class of modules which are proper generalization of both the purely extending modules and -extending modules. We call an -module is purely Goldie extending if, for each , there is a pure submodule P of such that . Many c
... Show MoreThe concept of fully pseudo stable Banach Algebra-module (Banach A-module) which is the generalization of fully stable Banach A-module has been introduced. In this paper we study some properties of fully stable Banach A-module and another characterization of fully pseudo stable Banach A-module has been given.
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In this paper, we proved coincidence points theorems for two pairs mappings which are defined on nonempty subset in metric spaces by using condition (1.1). As application, we established a unique common fixed points theorems for these mappings by using the concept weakly compatible (R-weakly commuting) between these mappings.
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The concept of epiform modules is a dual of the notion of monoform modules. In this work we give some properties of this class of modules. Also, we give conditions under which every hollow (copolyform) module is epiform.
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Let R be a commutative ring with unity .M an R-Module. M is called coprime module (dual notion of prime module) if ann M =ann M/N for every proper submodule N of M In this paper we study coprime modules we give many basic properties of this concept. Also we give many characterization of it under certain of module.