A study on dual square free modules
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=⨁i∈IMi 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 i∈I and, Mi and ⨁j≠iMj 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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PDFDOI: http://dx.doi.org/10.12958/adm1512
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