Glasgow Mathematical Journal

Research Article

Some properties of non-commutative regular graded rings

Thierry Levasseura1

a1 Département de Mathématiques, Université de Bretagne Occidentale, 6, Avenue Victor Le Gorgeu, 29287 Brest Cedex, France

Let A be a noetherian ring. When A is commutative (of finite Krull dimension), A is said to be Gorenstein if its injective dimension is finite. If A has finite global dimension, one says that A is regular. If A is arbitrary, these hypotheses are not sufficient to obtain similar results to those of the commutative case. To remedy this problem, M. Auslander has introduced a supplementary condition. Before stating it, we recall that the grade of a finitely generated (left or right) module is defined by

S0017089500008843_eqnU1

(Received March 26 1991)