Tohoku Mathematical Journal
2026
June
SECOND SERIES VOL. 78, NO. 2

Tohoku Math. J.
78 (2026), 243-267

Title ON A GENERALIZATION OF ULRICH MODULES AND ITS APPLICATIONS

Author Ela Celikbas, Olgur Celikbas, Justin Lyle, Ryo Takahashi and Yongwei Yao

(Received March 4, 2024, revised October 24, 2024)
Abstract. We study a modified version of the classical Ulrich modules, which we call $c$-Ulrich. Unlike the traditional setting, $c$-Ulrich modules always exist. We prove that these modules retain many of the essential properties and applications observed in the literature. Additionally, we reveal their significance as obstructions to Cohen-Macaulay properties of tensor products. Leveraging this insight, we show the utility of these modules in testing the finiteness of homological dimensions across various scenarios.

Mathematics Subject Classification. Primary 13C13; Secondary 13C14, 13D07.
Key words and phrases. Ulrich module, Cohen-Macaulay module, rigidity, test module, torsion, Hilbert-Samuel multiplicity, Betti numbers.

To the top of this page

Back to the Contents