Displaying similar documents to “ n -flat and n -FP-injective modules”

Bounds on Bass numbers and their dual

Abolfazl Tehranian, Siamak Yassemi (2007)

Archivum Mathematicum

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Let ( R , 𝔪 ) be a commutative Noetherian local ring. We establish some bounds for the sequence of Bass numbers and their dual for a finitely generated R -module.

The existence of envelopes

Edgar E. Enochs, Overtoun M. G. Jenda, Jinzhong Xu (1993)

Rendiconti del Seminario Matematico della Università di Padova

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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...