On reduction numbers and Castelnuovo–Mumford regularity of blowup rings and modules
CB Miranda-Neto, DS Queiroz - Collectanea Mathematica, 2024 - Springer
We prove new results on the interplay between reduction numbers and the Castelnuovo–
Mumford regularity of blowup algebras and blowup modules, the key basic tool being the …
Mumford regularity of blowup algebras and blowup modules, the key basic tool being the …
The set of trace ideals of curve singularities
T Kobayashi, S Kumashiro - Israel Journal of Mathematics, 2024 - Springer
We investigate a problem of when commutative local domains have a finite number of trace
ideals. The problem is left for the case of dimension one. In this paper, with a necessary …
ideals. The problem is left for the case of dimension one. In this paper, with a necessary …
On the reducing projective dimension over local rings
O Celikbas, S Dey, T Kobayashi… - Glasgow Mathematical …, 2024 - cambridge.org
In this paper, we are concerned with certain invariants of modules, called reducing
invariants, which have been recently introduced and studied by Araya–Celikbas and Araya …
invariants, which have been recently introduced and studied by Araya–Celikbas and Araya …
Tensor products and solutions to two homological conjectures for Ulrich modules
C Miranda-Neto, T Souza - Proceedings of the American Mathematical …, 2024 - ams.org
We address the problem of when the tensor product of two finitely generated modules over a
Cohen-Macaulay local ring is Ulrich in the generalized sense of Goto et al., and in particular …
Cohen-Macaulay local ring is Ulrich in the generalized sense of Goto et al., and in particular …
Reflexive modules over the endomorphism algebras of reflexive trace ideals
N Endo, S Goto - Journal of Pure and Applied Algebra, 2024 - Elsevier
In the present paper we investigate reflexive modules over the endomorphism algebras of
reflexive trace ideals in a one-dimensional Cohen-Macaulay local ring. The main theorem …
reflexive trace ideals in a one-dimensional Cohen-Macaulay local ring. The main theorem …
On a generalized Auslander-Reiten conjecture
It is well-known that the generalized Auslander-Reiten condition (GARC) and the symmetric
Auslander condition (SAC) are equivalent, and (GARC) implies that the Auslander-Reiten …
Auslander condition (SAC) are equivalent, and (GARC) implies that the Auslander-Reiten …