A local Cohen--Macaulay ring is called Ulrich-split if any short exact sequence of Ulrich
modules split. In this paper we initiate the study of Ulrich split rings. We prove several …

A semidualizing module is a generalization of Grothendieck's dualizing module. For a local
Cohen-Macaulay ring $ R $, the ring itself and its canonical module are always realized as …

We investigate relative cohomology functors on subcategories of abelian categories via
Auslander-Buchweitz approximations and the resulting strict resolutions. We verify that …

A degree of a module $ M $ is a numerical measure of information carried by $ M $. We
highlight some of Vasconcelos' outstanding contributions to the theory of degrees, bridging …

Let R be a commutative local Noetherian ring. We prove that the existence of a chain of
semidualizing R-complexes of length. d C 1/yields a degree-d polynomial lower bound for …

Motivated by a recent result of Yoshino and the work of Bergh on reducible complexity, we
introduce reducing versions of invariants of finitely generated modules over local rings. Our …

COTORSION PAIRS ASSOCIATED WITH AUSLANDER CATEGORIES Page 1 ISRAEL
JOURNAL OF MATHEMATICS 174 (2009), 253–268 DOI: 10.1007/s11856-009-0113-y …

Let R be a commutative noetherian ring. The n-semidualizing modules of R are
generalizations of its semidualizing modules. We will prove some basic properties of n …

A Cohen–Macaulay algebra has only finitely many semidualizing modules Page 1 Math.
Proc. Camb. Phil. Soc. (2008), 145, 601 c 2008 Cambridge Philosophical Society doi:10.1017/S0305004108001552 …

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 showed that …