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N-Cotorsion Envelopes of Modules

Udhayakumar R, Biju V


In homological algebra, covers and envelopes of modules play an important role. The relative version of flat and cotorsion modules was introduced by Lee SB in 2001, Selvaraj et al., (2015) introduced the concept of n-flat covers of modules (where n>0 be a non negative integer(. The main aim of this paper is to introduce the concept of n-cotorsion envelopes of modules and show that there is a very close connection between n-flat covers and n-cotorsion envelopes. Throughout this paper the standard diagram chasing method is used. First we prove that Schanuel’s lemma version for n-flat covers and we show that for any ring R, every left R-module has n-cotorsion envelope if and only if every left R-module has n-flat cover and let R be right n-coherent. If M has an n-flat cover, then M has an n-cotorsion envelope. n-flat covers of modules and n-cotorsion envelopes of modules are two interesting concepts in homological algebra. This paper gives a relationship between n-flat covers and n-cotorsion envelopes.

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