Some remarks on cotorsion envelopes of modules
Bull. Korean Math. Soc. 2007 Vol. 44, No. 4, 589-596
Published online December 1, 2007
Hae-sik Kim, Yeong-moo Song
Kyungpook National University, Sunchon National University
Abstract : In this paper we prove that the extension of pure injective module is pure injective if and only if the cotorsion envelope and the pure injective envelope of any $R$-module $M$ are isomorphic over $M$. And we prove that if the product of pure injective envelopes of flat modules is a pure injective envelope and the product of flat covers is a flat cover, then the product of cotorsion envelopes is a cotorsion envelope.
Keywords : flat cover, pure injective envelope, cotorsion envelope
MSC numbers : 16D80, 16E30
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