11 citations · 32 across the 32 of their papers we have counts for
5 papers · 1 filter
On generalized Gorenstein local rings
Shiro Goto, Shinya Kumashiro
In this paper, we introduce generalized Gorenstein local (GGL) rings. The notion of GGL rings is a natural generalization of the notion of almost Gorenstein rings, which can thus b…
On a generalized Auslander-Reiten conjecture
Souvik Dey, Shinya Kumashiro, Parangama Sarkar
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 con…
On the sectional genera and Cohen-Macaulay rings
Shinya Kumashiro, Hoang Le Truong, Hoang Ngoc Yen
We explore the behavior of the sectional genera of certain primary ideals in Noetherian local rings. In this paper, we provide characterizations of a Cohen-Macaulay local ring in t…
The set of trace ideals of curve singularities
Toshinori Kobayashi, Shinya Kumashiro
This paper mainly focuses on commutative local domains of dimension one. We then obtain a criterion for a ring to have a finite number of trace ideals in terms of integrally closed…
Upper bound on the colength of the trace of the canonical module in dimension one
Jürgen Herzog, Shinya Kumashiro
We study the upper bound of the colength of trace of the canonical module in one-dimensional Cohen-Macaulay rings. We answer the two questions posed by Herzog-Hibi-Stamate and Koba…