EPI-RETRACTABLE MODULES AND SOME APPLICATIONS

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GHORBANI A.; VEDADI M.R.

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Journal: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY Year:2009 | Volume:35 | Issue:1 Page(s): 155-166

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Title

EPI-RETRACTABLE MODULES AND SOME APPLICATIONS

Author(s)

GHORBANI A. | VEDADI M.R. | Issue Writer Certificate

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Abstract

Generalizing concepts “right Bezout ” and “principal right ideal ” of a ring R to modules, an R-module M is called n-epiretractable (resp. epi-retractable) if every n-generated submodule (resp. submodule) of MR is a homomorphic image of M. It is shown that if MR is finitely generated quasi-projective 1-epi-retractable, then EndR(M) is a right Bezout (resp. principal right ideal) ring if and only if MR is n-epi-retractable for all n³1 (resp. epiretractable). For a ring R and an infinite ordinal b³|R|, the R-module M = FÅN is epi-retractable where F is a free R-module with a basis set of cardinality b and N is a g-generated R-module with g£b. A ring R is quasi Frobenius if every injective R-module is epi-retractable. Injective modules in s[NR] are epi-retractable for every NÎs [MR] if and only if every non-zero factor ring of S is a quasi Frobenius ring where S is an endomorphism ring of a progenerator in s[MR].

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APA: Copy

GHORBANI, A., & VEDADI, M.R.. (2009). EPI-RETRACTABLE MODULES AND SOME APPLICATIONS. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 35(1), 155-166. SID. https://sid.ir/paper/562751/en

Vancouver: Copy

GHORBANI A., VEDADI M.R.. EPI-RETRACTABLE MODULES AND SOME APPLICATIONS. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY[Internet]. 2009;35(1):155-166. Available from: https://sid.ir/paper/562751/en

IEEE: Copy

A. GHORBANI, and M.R. VEDADI, “EPI-RETRACTABLE MODULES AND SOME APPLICATIONS,” BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol. 35, no. 1, pp. 155–166, 2009, [Online]. Available: https://sid.ir/paper/562751/en

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