60 citations · 392 across the 111 of their papers we have counts for
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On a generalization of Ulrich modules and its applications
Ela Celikbas, Olgur Celikbas, Justin Lyle +2
We study a modified version of the classical Ulrich modules, which we call -Ulrich. Unlike the traditional setting, -Ulrich modules always exist. We prove that these modules…
Ring homomorphisms and local rings with quasi-decomposable maximal ideal
Saeed Nasseh, Keri Ann Sather-Wagstaff, Ryo Takahashi
The notion of local rings with quasi-decomposable maximal ideal was formally introduced by Nasseh and Takahashi. In separate works, the authors of the present paper show that such…
Cofiniteness of local cohomology modules and subcategories of modules
Ryo Takahashi, Naoki Wakasugi
Let be a commutative noetherian ring and an ideal of . Assume that for all integers the local cohomology module is -cofinite. Suppose that $R_\mathfrak…
Annihilators and decompositions of singularity categories
Özgür Esentepe, Ryo Takahashi
Given any commutative Noetherian ring and an element in , we consider the full subcategory $\C(x)$ of its singularity category consisting of objects for which the morphi…