An extension is given of the theorem relating projective dimension to depth for a finitely
generated module of finite projective dimension over a commutative Noetherian local ring …

A question of Avramov and Foxby concerning injective dimension of complexes is settled in
the affirmative for the class of noetherian rings. A key step in the proof is to recast the …

Introduction. If P is a ring and M a left P-module, then homological alge-bra attaches three
dimensions to M, projective, weak, and injective (1)-By taking the supremum of one of these …

These notes were prepared for a series of ten lectures given at Regional Conference of the
Conference Board of the Mathematical Sciences in June 1971. The bulk of the lectures were …

Introduction. Among Noetherian rings quasi-Frobenius rings are those which are self
injective [10, Theorem 18]. This paper is concerned primarily with Noetherian rings whose …

If R is a ring with unit and A is a unitary left R-module, then homological. algebra attaches
three dimensions to A-projec-tive, weak, and injective. By taking the supremum of one of the …

This note presents the definitions of homological dimensions of bounded complexes of
modules as proposed by the author in [3]. Somewhat different definitions have been …

Introduction. This paper is devoted primarily to the study of commuta-tive noetherian local
rings. The main task is to compare purely algebraic properties with properties of a …

An example is given of a semiprimary ring with infinite finitistic dimension. The construction
shows that the global dimensions of finite dimensional algebras of finite global dimension …

We prove that (a) if R is a commutative coherent ring, the weak global dimension of R equals
the supremum of the flat (or (FP–) injective) dimensions of the simple R-modules;(b) if R is …