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PS-Lifting Modules
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DOI：10.1007/s11253-026-02555-y.png)
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Abstract
En 中文
Let R be a ring and M be a left R-module. We call M ps-lifting every submodule N of M containsa direct summand X of M such that NX\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{N}{X}$$\end{document} is projective semisimple. In this paper, we provide some properties of these modules. It is shown that: (1) if a projective module is ps-lifting, then it is hereditary; (2) for a ring R, every left R-module is ps-lifting if and only if every R-module is a direct sum of an injective module and a projective semisimple module; (3) RR is ps-lifting if and only if RSocR\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{R}{\text{Soc}\left(R\right)}$$\end{document} is semisimple and R is hereditary.
Keywords:
SEMIPERFECT