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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, \(\gamma \)-H-supplemented provided for every submodule N of M there is a direct summand D of M such that \(M=N+X\) if and only if \(M=D+X\) for every submodule X of M with M/X noncosingular. We prove that M is \(\gamma \)-H-supplemented if and only if for every submodule N of M there exists a direct summand D of M such that \((N+D)/N\ll _{\gamma } M/N\) and \((N+D)/D\ll _{\gamma } M/D\).

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  1. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

    Ali Reza Moniri Hamzekolaee

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  1. Ali Reza Moniri Hamzekolaee
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Correspondence to Ali Reza Moniri Hamzekolaee.

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Hamzekolaee, A.R.M. An approach to H-supplemented modules via noncosingular modules. Ann Univ Ferrara 67, 111–120 (2021). https://doi.org/10.1007/s11565-021-00356-8

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  • DOI: https://doi.org/10.1007/s11565-021-00356-8

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