Multiplicities of semidualizing modules
SM Cooper, S Sather-Wagstaff - Communications in Algebra, 2013 - Taylor & Francis
A finitely generated module C over a commutative noetherian ring R is semidualizing if Hom
R (C, C)≅ R and for all i≥ 1. For certain local Cohen–Macaulay rings (R, 𝔪), we verify the …
R (C, C)≅ R and for all i≥ 1. For certain local Cohen–Macaulay rings (R, 𝔪), we verify the …
Presentations of rings with non-trivial semidualizing modules
DA Jorgensen, GJ Leuschke… - Collectanea mathematica, 2012 - Springer
Let R be a commutative noetherian local ring. A finitely generated R-module C is
semidualizing if it is self-orthogonal and\rm Hom _R (C, C) ≅ R. We prove that a Cohen …
semidualizing if it is self-orthogonal and\rm Hom _R (C, C) ≅ R. We prove that a Cohen …
Semidualizing modules over numerical semigroup rings
E Celikbas, H Geller, T Kobayashi - arXiv preprint arXiv:2306.14989, 2023 - arxiv.org
A semidualizing module is a generalization of Grothendieck's dualizing module. For a local
Cohen-Macaulay ring $ R $, the ring itself and its canonical module are always realized as …
Cohen-Macaulay ring $ R $, the ring itself and its canonical module are always realized as …
Presentations of rings with a chain of semidualizing modules
E Amanzadeh, MT Dibaei - Mathematica Scandinavica, 2017 - JSTOR
Inspired by Jorgensen et al., it is proved that if a Cohen-Macaulay local ring R with dualizing
module admits a suitable chain of semidualizing R-modules of length n, then R≅ Q/(I₁+...+ …
module admits a suitable chain of semidualizing R-modules of length n, then R≅ Q/(I₁+...+ …
Tensor and torsion products of relative injective modules with respect to a semidualizing module
Let R be a commutative Cohen–Macaulay ring, and let C be a semidualizing module of R. In
this paper, we show that C is generically dualizing if and only if the tensor products of …
this paper, we show that C is generically dualizing if and only if the tensor products of …
Some criteria for regular and Gorenstein local rings via syzygy modules
D Ghosh - Journal of Algebra and Its Applications, 2019 - World Scientific
Let R be a Cohen–Macaulay local ring. We prove that the n th syzygy module of a maximal
Cohen–Macaulay R-module cannot have a semidualizing direct summand for every n≥ 1 …
Cohen–Macaulay R-module cannot have a semidualizing direct summand for every n≥ 1 …
On the self-dual maximal Cohen-Macaulay modules
A Ooishi - Journal of Pure and Applied Algebra, 1996 - Elsevier
We study the duality for maximal Cohen-Macaulay modules (MCM modules for short) over
Cohen-Macaulay local rings. We characterize (low dimensional) rings over which any MCM …
Cohen-Macaulay local rings. We characterize (low dimensional) rings over which any MCM …
[图书][B] Quasidualizing modules
BA Kubik - 2011 - search.proquest.com
We introduce and study" quasidualizing" modules over a commutative local noetherian ring
R. An artinian R-module T is quasidualizing if the homothety map [special characters …
R. An artinian R-module T is quasidualizing if the homothety map [special characters …
On the structure of the set of semidualizing complexes
A Gerko - Illinois Journal of Mathematics, 2004 - projecteuclid.org
We study the structure of the set of semidualizing complexes over a local ring. In particular,
we prove that for a pair of semidualizing complexes $ X_1 $ and $ X_2 $ such that $ G_ {X …
we prove that for a pair of semidualizing complexes $ X_1 $ and $ X_2 $ such that $ G_ {X …
Bass numbers and semidualizing complexes
S Sather-Wagstaff - Commutative algebra and its applications, 2009 - degruyter.com
Let R be a commutative local Noetherian ring. We prove that the existence of a chain of
semidualizing R-complexes of length. d C 1/yields a degree-d polynomial lower bound for …
semidualizing R-complexes of length. d C 1/yields a degree-d polynomial lower bound for …