FUNDAMENTAL DUALIZING COMPLEXES FOR COMMUTATIVE NOETHERIAN RINGS

1979 ◽  
Vol 30 (1) ◽  
pp. 21-32 ◽  
Author(s):  
JANET E. HALL
Keyword(s):  
Noetherian Rings ◽  
Dualizing Complexes

Dualizing complexes and flat homomorphisms of commutative Noetherian rings

1978 ◽  
Vol 84 (1) ◽  
pp. 37-45 ◽  
Author(s):  
Janet E. Hall ◽  
Rodney Y. Sharp
Keyword(s):  
Noetherian Rings ◽  
Ring Homomorphisms ◽  
Dualizing Complexes ◽  
Identity Elements

All rings considered in this paper will be commutative and Noetherian, will have identities, and will be assumed to be non-trivial unless otherwise specified. The letter A will always denote such a ring. It is to be assumed that ring homomorphisms respect identity elements.

Dualizing complexes for commutative Noetherian rings

1975 ◽  
Vol 78 (3) ◽  
pp. 369-386 ◽  
Author(s):  
Rodney Y. Sharp
Keyword(s):  
Local Ring ◽  
Commutative Algebra ◽  
Present Author ◽  
Partial Solution ◽  
Noetherian Rings ◽  
Finitely Generated ◽  
Injective Dimension ◽  
Noetherian Local Ring ◽  
Dualizing Complexes

The theory of dualizing complexes of Grothendieck and Hartshorne ((5), chapter v) has turned out to be a useful tool even in commutative algebra. For instance, Peskine and Szpiro used dualizing complexes in their (partial) solution of Bass's conjecture concerning finitely-generated (f.-g.) modules of finite injective dimension over a Noetherian local ring ((7), chapitre I, §5); and the present author first obtained the results in (9) by using dualizing complexes.

Simple Noetherian Rings

1975 ◽  
Author(s):  
John Cozzens ◽  
CArl Faith
Keyword(s):  
Noetherian Rings

Localization in Noetherian Rings

1986 ◽  
Author(s):  
A. V. Jategaonkar
Keyword(s):  
Noetherian Rings

The converse to a well known theorem on Noetherian rings

1968 ◽  
Vol 177 (4) ◽  
pp. 278-282 ◽  
Author(s):  
Paul M. Eakin
Keyword(s):  
Noetherian Rings

scholarly journals Semi-dualizing complexes and their Auslander categories

2001 ◽  
Vol 353 (5) ◽  
pp. 1839-1883 ◽  
Author(s):  
Lars Winther Christensen
Keyword(s):  
Dualizing Complexes

scholarly journals Indecomposable modules over one-dimensional Noetherian rings

2007 ◽  
Vol 208 (2) ◽  
pp. 739-760 ◽  
Author(s):  
Meral Arnavut ◽  
Melissa Luckas ◽  
Sylvia Wiegand
Keyword(s):  
Noetherian Rings ◽  
Indecomposable Modules ◽  
One Dimensional

Dualizing Complexes of Affine Semigroup Rings

1990 ◽  
Vol 322 (2) ◽  
pp. 561 ◽  
Author(s):  
Uwe Schafer ◽  
Peter Schenzel
Keyword(s):  
Semigroup Rings ◽  
Affine Semigroup ◽  
Dualizing Complexes

scholarly journals A note on Noetherian orders in Artinian rings

1979 ◽  
Vol 20 (2) ◽  
pp. 125-128 ◽  
Author(s):  
A. W. Chatters
Keyword(s):  
Noetherian Ring ◽  
Quotient Ring ◽  
Triangular Matrix ◽  
Idempotent Element ◽  
Noetherian Rings ◽  
Central Idempotent ◽  
Matrix Rings ◽  
Regular Elements ◽  
Zero Divisors ◽  
Left And Right

Throughout this note, rings are associative with identity element but are not necessarily commutative. Let R be a left and right Noetherian ring which has an Artinian (classical) quotient ring. It was shown by S. M. Ginn and P. B. Moss [2, Theorem 10] that there is a central idempotent element e of R such that eR is the largest Artinian ideal of R. We shall extend this result, using a different method of proof, to show that the idempotent e is also related to the socle of R/N (where N, throughout, denotes the largest nilpotent ideal of R) and to the intersection of all the principal right (or left) ideals of R generated by regular elements (i.e. by elements which are not zero-divisors). There are many examples of left and right Noetherian rings with Artinian quotient rings, e.g. commutative Noetherian rings in which all the associated primes of zero are minimal together with full or triangular matrix rings over such rings. It was shown by L. W. Small that if R is any left and right Noetherian ring then R has an Artinian quotient ring if and only if the regular elements of R are precisely the elements c of R such that c + N is a regular element of R/N (for further details and examples see [5] and [6]). By the largest Artinian ideal of R we mean the sum of all the Artinian right ideals of R, and it was shown by T. H. Lenagan in [3] that this coincides in any left and right Noetherian ring R with the sum of all the Artinian left ideals of R.

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