Residually faithful modules and the Cohen-Macaulay type of idealizations

2018/04/21 by Goto, Shiro, Kumashiro, Shinya, Loan, Nguyen Thi Hong · 1 citation
#13H10 #13H15 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.07885

Abstract

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 related to the theory of Ulrich modules \citeBHU, GOTWY1, GOTWY2, GTT2, and the other one is closely related to the theory of residually faithful modules and the theory of closed ideals \citeBV.

Cited by

• Characterization of almost Gorenstein rings in terms of the trace ideal

Related

• Two theorems about maximal Cohen-Macaulay modules
• Cohen-Macaulay test ideals over rings of finite and countable Cohen-Macaulay type
• Syzygies of Cohen-Macaulay modules over one dimensional Cohen-Macaulay local rings
• Approximations by maximal Cohen-Macaulay modules
• The structure of preenvelopes with respect to maximal Cohen-Macaulay modules