Flat envelopes in commutative rings Page 1 ISRAEL JOURNAL OF MATHEMATICS, Vol. 62,
No, 1, 1988 FLAT ENVELOPES IN COMMUTATIVE RINGS BY J. ASENSIO MAYOR AND J …

Let R be a ring (with identity). We shall call R a local ring if R is aright noetherian ring such
that the Jacobson radical M is a maximal ideal (and so is the only maximal ideal), and R/M is …

If S is a commutative, Noetherian local ring, it is well-known that S has finite global
dimension o S is a regular local ring. In particular, if S is not a domain, it must have infinite …

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 …

We prove that (a) if R is a left coherent ring, then the weak global dimension w D (R)<= n
(n>= 2) if and only if every (n–2) th F–cosyzygy of a finitely presented right R–module has a …

It is well known that a commutative, local, noetherian ring (with 1) of finite global dimension
must be a domain (indeed a regular local ring). For commutative local rings which are …

We define a dimension, called the finitely presented dimension, for modules and
commutative rings. This dimension has nice properties when the ring in question is …

The injective hull of a module M can be characterized as a homomorphism f: M~ E (with E an
injective module) such that for each homomorphism g: M--* E'with E'injective, there exists a …

The flat dimensions of injective modules Page 1 manuscripta math. 78, 165- 177 (1993)
manuscripta mathematica Spfinger-Verlag 1~3 THE FLAT DIMENSIONS OF INJECTIVE …

Let R be a commutative ring and let k be a positive integer. Following IS Cohen [6] we say
that R has rank k if each ideal of R has a basis of k elements (and hence R has rank s for …