11 citations · 32 across the 32 of their papers we have counts for
3 papers · 1 filter
Residually faithful modules and the Cohen-Macaulay type of idealizations
Shiro Goto, Shinya Kumashiro, Nguyen Thi Hong Loan
The Cohen-Macaulay type of idealizations of maximal Cohen-Macaulay modules over Cohen-Macaulay local rings is explored. There are two extremal cases, one of which is closely relate…
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…