Dual Sonlu Yarı Basit Yükseltilebilir Modüller

Year 2023, Volume: 28 Issue: 2, 424 - 431, 31.08.2023

Figen Eryılmaz

https://doi.org/10.53433/yyufbed.1143435

Abstract

$N\,P-$modülünün dual sonlu her $S$ alt modülü $N=U'\oplus V,\,\,U'\subseteq S$ve $S\cap V\subseteq Soc_{s}(V)$olacak şekilde bir ayrışıma sahip ise $N\,R-$modülüne dual sonlu yarı basit yükseltilebilir modül veya kısaca dual sonlu ss-yükseltilebilir modül denir. Bu çalışmada, bu tanıma denk koşullar verilmiştir. Buna ek olarak, makalede tanımlanan bu kavramın basit özellikleri incelenmiştir.

Keywords

Dual sonlu ss-yükseltilebilir modül, ss-tümlenmiş modül, Yarı basit modül

Cofinitely Semisimple (ss-) Lifting Modules

Abstract

An $P-$module $N$ is named cofinitely semisimple lifting or briefly cofinitely $ss-$lifting if for each cofinite submodule $S$ of $N$, $N$ has a decomposition $N=U'\oplus V$ such that $U'\subseteq S$ and $S\cap V\subseteq Soc_{s}(V)$. In this study, equivalent conditions to this definition are given. In addition, the basic features of this concept defined in this article are examined.

Keywords

Cofinitely ss-lifting module, Semisimple module, ss-supplemented module

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