A KIND OF F-INVERSE SPLIT MODULES

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Hosseinpour Mehrab; MONIRI HAMZEKOLAEE ALI REZA

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Journal: JOURNAL OF ALGEBRAIC SYSTEMS Year:2020 | Volume:7 | Issue:2 Page(s): 167-178

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Title

A KIND OF F-INVERSE SPLIT MODULES

Author(s)

Hosseinpour Mehrab | MONIRI HAMZEKOLAEE ALI REZA | Issue Writer Certificate

Keywords

Rickart module;Z(M)

inverse split module;Z^2(M)

inverse split module

Abstract

Let M be a right module over a ring R. In this manuscript, we shall study on a special case of F-inverse split modules where F is a fully invariant submodule of M introduced in [12]. We say M is Z 2(M)-inverse split provided f^(-1)(Z2(M)) is a direct summand of M for each endomorphism f of M. We prove that M is Z2(M)-inverse split if and only if M is a direct sum of Z2(M) and a Z2-torsionfree Rickart submodule. It is shown under some assumptions that the class of right perfect rings R for which every right R-module M is Z2(M)-inverse split (Z(M)-inverse split) is precisely that of right GV-rings.

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APA: Copy

Hosseinpour, Mehrab, & MONIRI HAMZEKOLAEE, ALI REZA. (2020). A KIND OF F-INVERSE SPLIT MODULES. JOURNAL OF ALGEBRAIC SYSTEMS, 7(2 ), 167-178. SID. https://sid.ir/paper/268355/en

Vancouver: Copy

Hosseinpour Mehrab, MONIRI HAMZEKOLAEE ALI REZA. A KIND OF F-INVERSE SPLIT MODULES. JOURNAL OF ALGEBRAIC SYSTEMS[Internet]. 2020;7(2 ):167-178. Available from: https://sid.ir/paper/268355/en

IEEE: Copy

Mehrab Hosseinpour, and ALI REZA MONIRI HAMZEKOLAEE, “A KIND OF F-INVERSE SPLIT MODULES,” JOURNAL OF ALGEBRAIC SYSTEMS, vol. 7, no. 2 , pp. 167–178, 2020, [Online]. Available: https://sid.ir/paper/268355/en

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