A calculation of injective dimension over valuation domains
A Change of Ring Theorem with Applications to Poincaré Series and Intersection Multiplicity.
A General Resolution for Grade Four Gorenstein Ideals.
A note on PG-modules.
A note on the Stanley-Reisner ring of a join and of a suspension.
A remark on Koszul complexes.
A variant theory for the Gorenstein flat dimension
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
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 is a ring extension such that for some regular element of , then is a G-ring if and only if so is . 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.
Amplitude inequalities for complexes
An axiomatic approach to homological dimension.
Anneaux cohérents de dimension homologique finie
Balanced projective dimension of modules
Characterizations of some rings with -projective, -(FP)-injective and -flat modules
Let be a commutative ring and a semidualizing -module. We investigate the relations between -flat modules and -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
Cohomological Dimension of Local Fields.
Complete intersection dimension
Contracting endomorphisms and dualizing complexes
We investigate how one can detect the dualizing property for a chain complex over a commutative local Noetherian ring . Our focus is on homological properties of contracting endomorphisms of , e.g., the Frobenius endomorphism when contains a field of positive characteristic. For instance, in this case, when is -finite and is a semidualizing -complex, we prove that the following conditions are equivalent: (i) is a dualizing -complex; (ii) for some ; (iii) and is derived -reflexive...
Decomposition of finitely generated modules using Fitting ideals
Let be a commutative Noetherian ring and be a finitely generated -module. The main result of this paper is to characterize modules whose first nonzero Fitting ideal is a product of maximal ideals of , in some cases.
Differentielle Eigenschaften der Lokalisierungen analytischer Algebren.