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2014, Springer Proceedings in Mathematics & Statistics, ISBN 9781493906260, Volume 76
Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between... 
Algebra | Mathematics | Geometry, algebraic
Web Resource
Journal of the London Mathematical Society, ISSN 0024-6107, 08/2017, Volume 96, Issue 1, pp. 271 - 292
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 09/2016, Volume 220, Issue 9, pp. 3067 - 3087
We investigate the behavior of four coherent-like conditions in regular conductor squares. In particular, we find necessary and sufficient conditions in order... 
Journal Article
Illinois Journal of Mathematics, ISSN 0019-2082, 06/2019, Volume 63, Issue 1, pp. 165 - 191
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 11/2017, Volume 145, Issue 11, pp. 4661 - 4674
Consider a non-trivial fiber product R=S\times _kT of local rings S, T with common residue field k. Given two finitely generated R-modules M and N, we show... 
Ext-index | Tor-vanishing | Semidualizing complexes | Ext-vanishing | Projective dimension | Auslander-Reiten | Fiber product | Injective dimension | MATHEMATICS, APPLIED | REGULAR LOCAL-RINGS | EXTENSIONS | AUSLANDER | semidualizing complexes | projective dimension | CATEGORIES | DUALIZING COMPLEXES | CONJECTURE | MATHEMATICS | ALGEBRAS | MODULES | RIGIDITY | REITEN | injective dimension | fiber product
Journal Article
Communications in Algebra, ISSN 0092-7872, 06/2017, Volume 45, Issue 6, pp. 2569 - 2592
Let X be a chain complex over a commutative noetherian ring R, that is, an object in the derived category (R). We investigate the small support and co-support... 
local cohomology | local homology | 13D09 | Adically finite complexes | 13B35 | 13D45 | cofinite complexes; derived categories; Koszul homology | 13J10 | 13D02 | MATHEMATICS | MODULES | COHOMOLOGY | cofinite complexes | COMPLETION | derived categories | COFINITE | HOMOLOGY | Koszul homology | Mathematical analysis | Homology | Algebra | Computation | Categories | Constrictions | Chains | Image detection | Rings (mathematics)
Journal Article
Journal of Algebra, ISSN 0021-8693, 11/2019, Volume 538, pp. 232 - 252
We continue our study of ladder determinantal rings over a field from the perspective of semidualizing modules. In particular, given a ladder of variables , we... 
Ladder determinantal ring | Semidualizing module | Gorenstein ring
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 4/2008, Volume 77, Issue 2, pp. 481 - 502
We show that an iteration of the procedure used to define the Gorenstein projective modules over a commutative ring R yields exactly the Gorenstein projective... 
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 08/2017, Volume 96, Issue 1, pp. 271 - 292
We apply geometric techniques from representation theory to the study of homologically finite differential graded (DG) modules M over a finite dimensional,... 
13E10 | 13D09 | 14L30 | 16G30 (primary) | 13D02 | MATHEMATICS | RING HOMOMORPHISMS | REFLEXIVITY | GORENSTEIN MODULES | COMPLEXES
Journal Article
Communications in Algebra, ISSN 0092-7872, 10/2017, Volume 45, Issue 10, pp. 4466 - 4476
Let M and N be differential graded (DG) modules over a positively graded commutative DG algebra A. We show that the Ext-groups defined in terms of... 
differential graded modules | 13D09 | Differential graded algebras | 13D07 | Yoneda Ext | 13D02 | MATHEMATICS | Modules | Algebra | Group theory
Journal Article
Communications in Algebra, ISSN 0092-7872, 09/2017, Volume 45, Issue 9, pp. 3893 - 3916
We prove the versions of amplitude inequalities of Iversen, Foxby and Iyengar, and Frankild and Sather-Wagstaff that replace finite generation conditions with... 
flat dimension | Adic finiteness | 13D09 | 13D07 | co-support | 13C12 | projective dimension | Frobenius endomorphism | injective dimension | amplitude inequality | support | 13D05 | COFINITE COMPLEXES | AMPLITUDE | CATEGORIES | MATHEMATICS | DIMENSIONS | MODULES | UNBOUNDED COMPLEXES | LOCAL COHOMOLOGY | Mathematical analysis | Homology | Inequalities | Algebra | Amplitudes | Rings (mathematics)
Journal Article
Algebras and Representation Theory, ISSN 1386-923X, 4/2019, Volume 22, Issue 2, pp. 297 - 319
Over a noetherian ring, it is a classic result of Matlis that injective modules admit direct sum decompositions into injective hulls of quotients by prime... 
13D07 | Gorenstein injective modules | Non-associative Rings and Algebras | 13C12 | Commutative Rings and Algebras | 13C13 | Mathematics | Filtrations | Semidualizing modules | 13C05 | Associative Rings and Algebras | Bass classes | Direct sum decompositions | Tensor products | MATHEMATICS | DIMENSIONS | FINITENESS
Journal Article
Algebras and Representation Theory, ISSN 1386-923X, 10/2016, Volume 19, Issue 5, pp. 1217 - 1238
We present an in-depth exploration of the module structures of local (co)homology modules (moreover, for complexes) over the completion R ̑ 𝔞 $\widehat... 
13D09 | Support | Non-associative Rings and Algebras | 13B35 | 13C12 | Commutative Rings and Algebras | Derived local homology | 13D45 | Mathematics | Adic finiteness | Associative Rings and Algebras | MGM equivalence | Greenlees-May duality | Cohomologically cofinite complexes | Derived local cohomology | MATHEMATICS | RESOLUTIONS
Journal Article
Glasgow Mathematical Journal, ISSN 0017-0895, 01/2015, Volume 57, Issue 1, pp. 231 - 240
Given a finitely generated module over a commutative noetherian ring that satisfies certain reflexivity conditions, we show how failure of the semidualizing... 
SEMIDUALIZING COMPLEXES | MATHEMATICS | RING HOMOMORPHISMS | DIMENSION | Mathematics | Mathematical analysis | Modules | Failure | Disengaging | Rings (mathematics)
Journal Article
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, ISSN 0035-7596, 2018, Volume 48, Issue 3, pp. 947 - 965
Motivated by work of Hochster and Huneke, we investigate several constructions related to the S-2-ification T of a complete equidimensional local ring R: the... 
MATHEMATICS | S-2-ifications | connected components | CONNECTEDNESS | graph labeling | monomial ideals | canonical modules
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 12/2017, Volume 16, Issue 12
We investigate the similarities between adic finiteness and homological finiteness for chain complexes over a commutative Noetherian ring. In particular, we... 
derived local homology | Adic finiteness | co-support | derived local cohomology | support | MATHEMATICS, APPLIED | COFINITE | CATEGORIES | MATHEMATICS | MODULES | UNBOUNDED COMPLEXES | HOMOLOGY | LOCAL COHOMOLOGY
Journal Article
Communications in Algebra, ISSN 0092-7872, 06/2019, Volume 47, Issue 6, pp. 2341 - 2356
Conditions on the Koszul complex of a noetherian local ring R guarantee that is nonzero for infinitely many i, when M and N are finitely generated R-modules of... 
Local DG algebra | 13D40 (secondary) | vanishing of Tor | 13D07 (primary) | 16E45 | perfect DG module | 13D02 | MATHEMATICS | Homology | Modules
Journal Article
JOURNAL OF ALGEBRA, ISSN 0021-8693, 11/2019, Volume 538, pp. 232 - 252
We continue our study of ladder determinantal rings over a field k from the perspective of semidualizing modules. In particular, given a ladder of variables Y,... 
Ladder determinantal ring | MATHEMATICS | Gorenstein ring | Semidualizing module
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 09/2015, Volume 219, Issue 9, pp. 3889 - 3912
We introduce and study the weighted -path ideal of a weighted graph , which is a common generalization of Conca and De Negri's -path ideal for unweighted... 
MATHEMATICS | EDGE IDEALS | MATHEMATICS, APPLIED | MACAULAY
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 9/2014, Volume 103, Issue 3, pp. 211 - 218
Given a flat local ring homomorphism $${R \rightarrow S}$$ R → S and two finitely generated R-modules M and N, we describe conditions under which the modules... 
Ext | 13D07 | Ascent | Primary 13B40 | Flat homomorphism | Tor | Mathematics, general | NAK | Mathematics | Secondary 13D02 | MATHEMATICS
Journal Article
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