14 citations · 31 across the 13 of their papers we have counts for
13 papers
When is the strict closure of rings finitely generated?
Ryotaro Isobe
This paper investigates the finite generation of the strict closure of rings in arbitrary dimension. For a Noetherian local ring , we provide a sufficient condit…
Construction and finite generation of the strict closure of rings
Ryotaro Isobe
The construction of Arf rings and strictly closed rings has been studied widely; however, there has been no clear description of the structure of the strict closure R^* when the in…
Characterization of almost Gorenstein rings in terms of the trace ideal
Ryotaro Isobe, Shinya Kumashiro
We provide a characterization of one-dimensional almost Gorenstein rings in terms of the trace ideal. As an application, we investigate the almost Gorenstein property of certain $\…
Reflexive modules over Arf local rings
Ryotaro Isobe, Shinya Kumashiro
We provide a certain direct-sum decomposition of reflexive modules over (one-dimensional) Arf local rings. We also see the equivalence of three notions, say, integrally closed idea…
Topics on strict closure of rings
Naoki Endo, Shiro Goto, Ryotaro Isobe
In 1971, J. Lipman introduced the notion of strict closure of a ring in another, and established the underlying theory in connection with a conjecture of O. Zariski. In this paper,…
Decomposition of integrally closed ideals in Arf rings
Ryotaro Isobe
This study investigates the structure of Arf rings. From the perspective of ring extensions, a decomposition of integrally closed ideals is given. Using this, we present a kind of…
On the ubiquity of Arf rings
Ela Celikbas, Olgur Celikbas, Cătălin Ciupercă +4
We introduce and develop the theory of weakly Arf rings, which is a generalization of Arf rings, initially defined by J. Lipman in 1971. We provide characterizations of weakly Arf…
The Structure of Ulrich ideals in hypersurfaces
Ryotaro Isobe
This paper studies Ulrich ideals in hypersurface rings. A characterization of Ulrich ideals is given. Using the characterization, we construct a minimal free resolution of an Ulric…
Almost Gorenstein rings arising from fiber products
Naoki Endo, Shiro Goto, Ryotaro Isobe
The purpose of this paper is, as part of the stratification of Cohen-Macaulay rings, to investigate the question of when the fiber products are almost Gorenstein rings. We show tha…
Ulrich ideals and 2-AGL rings
Shiro Goto, Ryotaro Isobe, Naoki Taniguchi
The notion of 2-almost Gorenstein local ring (2-AGL ring for short) is a generalization of the notion of almost Gorenstein local ring from the point of view of Sally modules of can…
The structure of chains of Ulrich ideals in Cohen-Macaulay local rings of dimension one
Shiro Goto, Ryotaro Isobe, Shinya Kumashiro
This paper studies Ulrich ideals in one-dimensional Cohen-Macaulay local rings. A correspondence between Ulrich ideals and overrings is given. Using the correspondence, chains of U…
Correspondence between trace ideals and birational extensions with application to the analysis of the Gorenstein property of rings
Shiro Goto, Ryotaro Isobe, Shinya Kumashiro
Over an arbitrary commutative ring, correspondences among three sets, the set of trace ideals, the set of stable ideals, and the set of birational extensions of the base ring, are…
Characterization of generalized Gorenstein rings
Shiro Goto, Ryotaro Isobe, Shinya Kumashiro +1
The notion of generalized Gorenstein local ring (GGL ring for short) is one of the generalizations of Gorenstein rings. In this article, there is given a characterization of GGL ri…