$k$-torsionless modules with finite Gorenstein dimension

Maryam Salimi; Elham Tavasoli; Siamak Yassemi

Displaying similar documents to “ $k$ -torsionless modules with finite Gorenstein dimension”

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 $n \geq 0$ , we prove that ${l . id}_{R} (ω) = {r . id}_{S} (ω) \leq n$ 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...

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 $fd ({(_{R} R)}^{+}) \leq n$ 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 Cohen-Macaulay rings

Edgar E. Enochs, Jenda M. G. Overtoun (1994)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we use a characterization of $R$ -modules $N$ such that $f d_{R} N = p d_{R} N$ to characterize Cohen-Macaulay rings in terms of various dimensions. This is done by setting $N$ to be the $d t h$ local cohomology functor of $R$ with respect to the maximal ideal where $d$ is the Krull dimension of $R$ .

Displaying similar documents to “ k -torsionless modules with finite Gorenstein dimension”

Wakamatsu tilting modules with finite injective dimension

FC-modules with an application to cotorsion pairs

On Cohen-Macaulay rings

Displaying similar documents to “ $k$ -torsionless modules with finite Gorenstein dimension”