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This paper discusses a variant theory for the Gorenstein flat dimension. Actually, since it is not yet known whether the category (R) of Gorenstein flat modules over a ring R is projectively resolving or not, it appears legitimate to seek alternate ways of measuring the Gorenstein flat dimension of modules which coincide with the usual one in the case where (R) is projectively resolving, on the one hand, and present nice behavior for an arbitrary ring R, on the other. In this paper, we introduce...

About G-rings

Najib Mahdou (2017)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we are concerned with G-rings. We generalize the Kaplansky’s theorem to rings with zero-divisors. Also, we assert that if $R \subseteq T$ is a ring extension such that $m T \subseteq R$ for some regular element $m$ of $T$ , then $T$ is a G-ring if and only if so is $R$ . Also, we examine the transfer of the G-ring property to trivial ring extensions. Finally, we conclude the paper with illustrative examples discussing the utility and limits of our results.

Acyclicity versus total acyclicity for complexes over noetherian rings.

Iyengar, Srikanth, Krause, Henning (2006)

Documenta Mathematica

Amplitude inequalities for complexes

Birger Iversen (1977)

Annales scientifiques de l'École Normale Supérieure

An axiomatic approach to homological dimension.

Jack Ohm (1975)

Mathematica Scandinavica

Anneaux cohérents de dimension homologique finie

José Bertin (1972)

Publications mathématiques et informatique de Rennes

Balanced projective dimension of modules

Radoslav M. Dimitrić (1997)

Acta Mathematica et Informatica Universitatis Ostraviensis

Characterizations of some rings with $𝒞$ -projective, $𝒞$ -(FP)-injective and $𝒞$ -flat modules

Xiao Guang Yan, Xiao Sheng Zhu (2011)

Czechoslovak Mathematical Journal

Let $R$ be a commutative ring and $𝒞$ a semidualizing $R$ -module. We investigate the relations between $𝒞$ -flat modules and $𝒞$ -FP-injective modules and use these modules and their character modules to characterize some rings, including artinian, noetherian and coherent rings.

Cohen-Macaulay homological dimensions

Henrik Holm, Peter Jørgensen (2007)

Rendiconti del Seminario Matematico della Università di Padova

Cohomological Dimension of Local Fields.

Hanspeter Kraft (1973)

Mathematische Zeitschrift

Complete intersection dimension

Luchezar L. Avramov, Vesselin N. Gasharov, Irena V. Peeva (1997)

Publications Mathématiques de l'IHÉS

Contracting endomorphisms and dualizing complexes

Saeed Nasseh, Sean Sather-Wagstaff (2015)

Czechoslovak Mathematical Journal

We investigate how one can detect the dualizing property for a chain complex over a commutative local Noetherian ring $R$ . Our focus is on homological properties of contracting endomorphisms of $R$ , e.g., the Frobenius endomorphism when $R$ contains a field of positive characteristic. For instance, in this case, when $R$ is $F$ -finite and $C$ is a semidualizing $R$ -complex, we prove that the following conditions are equivalent: (i) $C$ is a dualizing $R$ -complex; (ii) $C \sim 𝐑 {Hom}_{R} (^{n} R, C)$ for some $n > 0$ ; (iii) $G_{C} {-dim}^{n} R < \infty$ and $C$ is derived $𝐑 {Hom}_{R} (^{n} R, C)$ -reflexive...

Decomposition of finitely generated modules using Fitting ideals

Somayeh Hadjirezaei, Sina Hedayat (2020)

Czechoslovak Mathematical Journal

Let $R$ be a commutative Noetherian ring and $M$ be a finitely generated $R$ -module. The main result of this paper is to characterize modules whose first nonzero Fitting ideal is a product of maximal ideals of $R$ , in some cases.

Differentielle Eigenschaften der Lokalisierungen analytischer Algebren.

Günter Scheja, Uwe Storch (1972)

Mathematische Annalen

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