In this article, the word" ring" will mean" commutative, Noetherian ring with non-zero
multiplicative identity", and it is to be understood that ring homomorphisms respect identity …

Let R be a commutative Noetherian ring. Let P (R)(respectively, I (R)) be the category of all
finite R-modules of finite projective (respectively, injective) dimension. Sharp [9] constructed …

LET A. he a noetherian local ring and t an indeterminate over A. In (1) it is shown that when
A is regular of dimension 1, the finitely generated projective A [£]-modules are free. We show …

All the rings considered in this paper will be commutative and have multiplicative identities.
Such a ring is called trivial if it consists of just one (zero) element: it is to be understood that …

IDEALS GENERATED BY THREE ELEMENTS idealI,d(R\l)=h. Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 35, No. 1, September 1972 IDEALS …

The starting point for the discussion in the present paper is another result of Levin and
Vasconcelos. In [13], Theorem 2.2, they proved that, if R is a Gorenstein local ring, then a fg …

1. Introduction. It has been noticed by the author and others that there are many ways in
which the homological dimension of a module can be defined. The author has noticed this …

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 …

The fimdam al result of AV Jategaonkar's im ortant paper is th, e following: If is a finitely
generated Noetherian ring, and) r is an essential submoduie of ml! dimens~ Q~ 4.2, then M …

ALL the rings considered in this note will be commutative and Noetherian and will have non-
zero multiplicative identities. A recent addition to the tools available for use in local algebra …