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The Torsion Theory Generated by <Emphasis Type="Italic">M</Emphasis>-Small Modules

Authors:	Email author" target="_blank">A??iгdem??zcan Email author Abdullah?Harmanci

Institution:	(1) Department of Mathematics, Haccttepe University, 06532 Beytepe, Ankara, Turkey

Abstract:	Let M be a right R-module, ${\cal M}$ the class of all M-small modules, and P a projective cover of M in $\sigma$ M]. We consider the torsion theories $\tau_{\cal M}$ = ( ${\cal T}_{\cal M}, {\cal F}_{\cal M}$ ), $\tau_V$ = ( ${\cal T}_V, {\cal F}_V$ ), and $\tau_P$ = ( ${\cal T}_P, {\cal F}_P$ ) in $\sigma$ M], where $\tau_{\cal M}$ is the torsion theory generated by ${\cal M}, \tau_V$ is the torsion theory cogenerated by ${\cal M}$ , and $\tau_P$ is the dual Lambek torsion theory. We study some conditions for $\tau_{\cal M}$ to be cohereditary, stable, or split, and prove that Rej(M, ${\cal M}$ ) = M $\Leftrightarrow$ ${\cal F}_P$ = ${\cal M}$ (= ${\cal T}_{\cal M}$ = ${\cal F}_V$ ) $\Leftrightarrow$ ${\cal T}_P$ = ${\cal T}_V$ $\Leftrightarrow$ Gen_M(P) $\subseteq$ ${\cal T}_V$ .2000 Mathematics Subject Classification: 16S90

Keywords:	hereditary torsion theory small module
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