An approach to H-supplemented modules via noncosingular modules

Hamzekolaee Ali Reza Moniri

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An approach to H-supplemented modules via noncosingular modules

机译：An approach to H-supplemented modules via noncosingular modules

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Abstract Let M be a module over a ring R. We call M, γdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$gamma $$end{document}-H-supplemented provided for every submodule N of M there is a direct summand D of M such that M=N+Xdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$M=N+X$$end{document} if and only if M=D+Xdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$M=D+X$$end{document} for every submodule X of M with M/X noncosingular. We prove that M is γdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$gamma $$end{document}-H-supplemented if and only if for every submodule N of M there exists a direct summand D of M such that (N+D)/N?γM/Ndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$(N+D)/Nll _{gamma } M/N$$end{document} and (N+D)/D?γM/Ddocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$(N+D)/Dll _{gamma } M/D$$end{document}.

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《Annali Dell Universita di Ferrara, Sezione VII. Scienze Matematiche》 |2021年第1期|111-120|共10页
作者
Hamzekolaee Ali Reza Moniri;
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University of Mazandaran;

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中图分类数学;
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γdocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$gamma $$end{document}-small submodule; H-supplemented module; γdocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$gamma $$end{document}-H-supplemented module; 16D10; 16D40; 16D80;

An approach to H-supplemented modules via noncosingular modules

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