 Generalization of $\mathcal{U}$-Generator and $M$-Subgenerator Related to Category $\sigma[M]$Fitriani Fitriani, Indah Wijayanti and Budi Surodjo Journal of Mathematics Research, 2018, vol. 10, issue 4, 101-106 Abstract: Let $\mathcal{U}$ be a non-empty set of $R$-modules. $R$-module $N$ is generated by $\mathcal{U}$ if there is an epimorphism from $\oplus_{\Lambda}U_{\lambda}$ to $N$, where $U_{\lambda} \in \mathcal{U}$, for every $\lambda \in \Lambda$. $R$-module $M$ is a subgenerator for $N$ if $N$ is isomorphic to a submodule of an $M$-generated module. In this paper, we introduce a $\mathcal{U}_{V}$-generator, where $V$ be a submo\-dule of $\oplus_{\Lambda}U_{\lambda}$, as a generalization of $\mathcal{U}$-generator by using the concept of $V$-coexact sequence. We also provide a $\mathcal{U}_{V}$-subgenerator motivated by the concept of $M$-subgenerator. Furthermore, we give some properties of $\mathcal{U}_{V}$-generated and $\mathcal{U}_{V}$-subgenerated modules related to category $\sigma[M]$. We also investigate the existence of pullback and pushout of a pair of morphisms of $\mathcal{U}_{V}$-subgenerated modules. We prove that the collection of $\mathcal{U}_{V}$-subgenerated modules is closed under submodules and factor modules. Keywords: $\mathcal{U}$-generator; $\mathcal{U}_{V}$-generator; V-coexact sequences; $M$-subgenerator; $\mathcal{U}_{V}$-subgenerator (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:10:y:2018:i:4:p:101 Access Statistics for this article More articles in Journal of Mathematics Research from Canadian Center of Science and Education Contact information at EDIRC. |
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