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A study on dual square free modules

M. Medina-Bárcenas, D. Keskin Tütüncü, Y. Kuratomi

Abstract


Let M be an H-supplemented coatomic module with FIEP. Then we prove that M is dual square free if and only if every maximal submodule of M is fully invariant. Let M=iIMi be a direct sum, such that M is coatomic. Then we prove that M is dual square free if and only if each Mi is dual square free for all iI and, Mi and jiMj are dual orthogonal. Finally we study the endomorphism rings of dual square free modules. Let M be a quasi-projective module. If EndR(M) is right dual square free, then M is dual square free. In addition, if M is finitely generated, then EndR(M) is right dual square free whenever M is dual square free. We give several examples illustrating our hypotheses.

Keywords


dual square free module, endoregular module, (finite) internal exchange property

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DOI: http://dx.doi.org/10.12958/adm1512

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