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math.AC2018
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…
math.AC2018
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…