Reflexive modules over Gorenstein rings
WV Vasconcelos - Proceedings of the American Mathematical Society, 1968 - JSTOR
Introduction. The aim of this paper is to show the relevance of a class of commutative
noetherian rings to the study of reflexive nmod-ules. They include integrally closed domains …
noetherian rings to the study of reflexive nmod-ules. They include integrally closed domains …
[引用][C] Gorenstein modules
RY Sharp - Mathematische Zeitschrift, 1970 - Springer
Throughout this paper, the word" ring" will mean" commutative,(associative,) Noetherian ring
with a non-zero multiplicative identity". In [9], I discussed the Cousin Complex, C (M), for a …
with a non-zero multiplicative identity". In [9], I discussed the Cousin Complex, C (M), for a …
[引用][C] Rings of type 1 are Gorenstein
P Roberts - Bulletin of the London Mathematical Society, 1983 - academic.oup.com
In the original paper on Gorenstein rings, Bass [1] characterizes Gorenstein rings as those
commutative Noetherian local rings A which are Cohen-Macaulay and satisfy nn {A)= 1 …
commutative Noetherian local rings A which are Cohen-Macaulay and satisfy nn {A)= 1 …
Vanishing of
S Goto - Journal of Mathematics of Kyoto University, 1982 - projecteuclid.org
In case A has finite Krull-dimension, say d, it is well-known by Bass [2] that A is a Gorenstein
ring if and only if ExtiA (M, A)=(0) for every finitely generated A-module M and for every …
ring if and only if ExtiA (M, A)=(0) for every finitely generated A-module M and for every …
[引用][C] Acceptable rings and homomorphic images of Gorenstein rings
RY Sharp - Journal of Algebra, 1977 - Elsevier
This paper is concerned with a new class of commutative Noetherian rings. Accordingly, all
the rings considered in this paper will be commutative and have multiplicative identities …
the rings considered in this paper will be commutative and have multiplicative identities …
[引用][C] Rings which are a factor of a Gorenstein ring by its socle
W Teter - Inventiones mathematicae, 1974 - Springer
The object of this article is to determine when a commutative Artin local ring A is the
homomorphic image ofa Gorenstein ring t F in such a way that the kernel of the …
homomorphic image ofa Gorenstein ring t F in such a way that the kernel of the …
Cyclic modules of finite Gorenstein injective dimension and Gorenstein rings
HB Foxby, AJ Frankild - Illinois Journal of Mathematics, 2007 - projecteuclid.org
The main result asserts that a local commutative Noetherian ring is Gorenstein, if it
possesses a non-zero cyclic module of finite Gorenstein injective dimension. From this …
possesses a non-zero cyclic module of finite Gorenstein injective dimension. From this …
[引用][C] Finitely Generated Modules of Finite Injective Dimension Over Certain Cohen‐Macaulay Rings†
RY Sharp - Proceedings of the London Mathematical Society, 1972 - Wiley Online Library
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 …
Vasconcelos. In [13], Theorem 2.2, they proved that, if R is a Gorenstein local ring, then a fg …
Foxby duality and Gorenstein injective and projective modules
E Enochs, O Jenda, J Xu - Transactions of the American Mathematical …, 1996 - ams.org
In 1966, Auslander introduced the notion of the $ G $-dimension of a finitely generated
module over a Cohen-Macaulay noetherian ring and found the basic properties of these …
module over a Cohen-Macaulay noetherian ring and found the basic properties of these …
The converse to a theorem of Sharp on Gorenstein modules
I Reiten - Proceedings of the American Mathematical Society, 1972 - ams.org
Let A be a commutative local Noetherian ring with identity of Krull dimension n, m its
maximal ideal. Sharp has proved that if A is Cohen-Macauley and a homomorphic image of …
maximal ideal. Sharp has proved that if A is Cohen-Macauley and a homomorphic image of …