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 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 Downloads: Full-text PDF