Construction of Auslander-Gorenstein local rings as Frobenius extensions. (English) Zbl 1357.16025
Summary: Starting from an arbitrary ring \(R\) we provide a systematic construction of \(\mathbb {Z}/n\mathbb {Z}\)-graded rings \(A\) which are Frobenius extensions of \(R\), and show that under mild assumptions, \(A\) is an Auslander-Gorenstein local ring if and only if so is \(R\).
MSC:
16E65 | Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) |
16L30 | Noncommutative local and semilocal rings, perfect rings |
16E10 | Homological dimension in associative algebras |