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.