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On the notion of Cohen–Macaulayness for non-Noetherian rings |
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| Authors: | Mohsen Asgharzadeh Massoud Tousi |
| Affiliation: | aDepartment of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran;bDepartment of Mathematics, Center of Excellence in Algebraic and Logical Structures in Discrete Mathematics, Shahid Beheshti University, G.C., Tehran, Iran;cSchool of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran |
| Abstract: | There exist many characterizations of Noetherian Cohen–Macaulay rings in the literature. These characterizations do not remain equivalent if we drop the Noetherian assumption. The aim of this paper is to provide some comparisons between some of these characterizations in non-Noetherian case. Toward solving a conjecture posed by Glaz, we give a generalization of the Hochster–Eagon result on Cohen–Macaulayness of invariant rings, in the context of non-Noetherian rings. |
| Keywords: | Cohen– Macaulay ring Grade of an ideal Height of an ideal Non-Noetherian ring Rings of invariants |
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