2017/12/05 by L. Fuchs, Fuchs, Laszlo, Bruce Olberding +1
Mathematics · #13H10 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1712.01753
openalex publication_date 2017/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new class of commutative non-noetherian rings, called n-subperfect rings, generalizing the almost perfect rings that have been studied recently by Fuchs-Salce. For an integer n ≥ 0, the ring R is n-subperfect if every maximal regular sequence in R has length n and the total ring of quotients of R/I for any ideal I generated by a regular sequence is a perfect ring in the sense of Bass. We define an extended Cohen-Macaulay ring as a commutative ring R that has noetherian prime spectrum and each localization RM at a maximal ideal M is ht(M)-subperfect. In the noetherian case, these are precisely the classical Cohen-Macaulay rings. Several relevant properties are proved reminiscent of those shared by Cohen-Macaulay rings.