Displaying similar documents to “ ( n , d ) -injective covers, n -coherent rings, and ( n , d ) -rings”

FC-modules with an application to cotorsion pairs

Yonghua Guo (2009)

Commentationes Mathematicae Universitatis Carolinae

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Let R be a ring. A left R -module M is called an FC-module if M + = Hom ℤ ( M , ℚ / ℤ ) is a flat right R -module. In this paper, some homological properties of FC-modules are given. Let n be a nonnegative integer and ℱ𝒞 n the class of all left R -modules M such that the flat dimension of M + is less than or equal to n . It is shown that ( ⊥ ( ℱ𝒞 n ⊥ ) , ℱ𝒞 n ⊥ ) is a complete cotorsion pair and if R is a ring such that fd ( ( R R ) + ) ≤ n and ℱ𝒞 n is closed under direct sums, then ( ℱ𝒞 n , ℱ𝒞 n ⊥ ) is a perfect cotorsion pair. In particular, some known results are obtained as...

On some classes of modules

Gonca Güngöroglu, Harmanci, Abdullah (2000)

Czechoslovak Mathematical Journal

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The aim of this paper is to investigate quasi-corational, comonoform, copolyform and α -(co)atomic modules. It is proved that for an ordinal α a right R -module M is α -atomic if and only if it is α -coatomic. And it is also shown that an α -atomic module M is quasi-projective if and only if M is quasi-corationally complete. Some other results are developed.

Wakamatsu tilting modules with finite injective dimension

Guoqiang Zhao, Lirong Yin (2013)

Czechoslovak Mathematical Journal

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Let R be a left Noetherian ring, S a right Noetherian ring and R ω a Wakamatsu tilting module with S = End ( R ω ) . We introduce the notion of the ω -torsionfree dimension of finitely generated R -modules and give some criteria for computing it. For any n ≥ 0 , we prove that l . id R ( ω ) = r . id S ( ω ) ≤ n if and only if every finitely generated left R -module and every finitely generated right S -module have ω -torsionfree dimension at most n , if and only if every finitely generated left R -module (or right S -module) has generalized Gorenstein...