… We prove that the trivial extension A ›<T is a quasi-Gorenstein ring if and … -Gorenstein rings
under flat base change. In section 3 we study the endomorphism ring of a canonical module. …

… We study the canonical trace for tensor products and Segre … Gorenstein Hibi rings. We study
connections between the class of nearly Gorenstein rings and that of almost Gorenstein rings…

… is given for type 2 rings. We also introduce the class of weakly almost Gorenstein rings
using the canonical module, and show that they are almost Gorenstein rings in dimension one, …

… For elementary properties of the canonical module, we refer the reader to[4, §6J, [5, 5 …
Gorenstein ring, R has the canonical module C and it is well known that C is the canonical module …

… given for type 2 rings. We also introduce the class of weakly almost Gorenstein rings using
the canonical module, and show that they are almost Gorenstein rings in dimension one, and …

… Let (R, m) be a local one-dimensional Cohen–Macaulay ring. We say that R is an almost
Gorenstein ring if it has a canonical module ωR which is isomorphic to a fractional ideal of R …

… totally reflexive R-modules. Over a Gorenstein ring, the totally reflexive modules are precisely
… maximal Cohen–Macaulay modules; hence, in particular, every singular Gorenstein local …

… local theory of the canonical module over a Cohen-Macaulay ring, and in particular we shall
study local Gorenstein rings-those local rings for which the canonical module is free. What …

… group algebra (which is a QF-ring), … module cat egories Mod(A) and Mod(A) of a ring A
from the point of view of modern algebraic homotopy theory. This is possible if the stable module …

… , by r(R) the Gorenstein type (in case R is Cohen-Macaulay), by Quot(R) the total ring of
quotients, and by o R the canonical module of R (provided the canonical module exists). …