scholarly journals New homological invariants for modules over local rings, II

2000 ◽  
Vol 153 (1) ◽  
pp. 65-78 ◽  
Author(s):  
Alex Martsinkovsky
Keyword(s):  
Local Rings ◽  
Homological Invariants

scholarly journals Homological Invariants of Local Rings

1963 ◽  
Vol 22 ◽  
pp. 219-227 ◽  
Author(s):  
Hiroshi Uehara
Keyword(s):  
Local Ring ◽  
Betti Numbers ◽  
Residue Field ◽  
Unit Element ◽  
Minimal System ◽  
Local Rings ◽  
Homology Algebra ◽  
Homological Invariants ◽  
Minimal System Of Generators ◽  
The Relationship

In this paper R is a commutative noetherian local ring with unit element 1 and M is its maximal ideal. Let K be the residue field R/M and let {t1,t2,…, tn) be a minimal system of generators for M. By a complex R<T1. . ., Tp> we mean an R-algebra* obtained by the adjunction of the variables T1. . ., Tp of degree 1 which kill t1,…, tp. The main purpose of this paper is, among other things, to construct an R-algebra resolution of the field K, so that we can investigate the relationship between the homology algebra H (R < T1,…, Tn>) and the homological invariants of R such as the algebra TorR(K, K) and the Betti numbers Bp = dimk TorR(K, K) of the local ring R. The relationship was initially studied by Serre [5].

scholarly journals Correction to: Classification of non-local rings with genus two zero-divisor graphs

2021 ◽  
Vol 25 (4) ◽  
pp. 3355-3356
Author(s):  
T. Asir ◽  
K. Mano ◽  
T. Tamizh Chelvam
Keyword(s):  
Zero Divisor ◽  
Local Rings ◽  
Non Local ◽  
Genus Two

scholarly journals Analytic ramifications and flat couples of local rings

1981 ◽  
Vol 146 (0) ◽  
pp. 201-208 ◽  
Author(s):  
Tomas Larfeldt ◽  
Christer Lech
Keyword(s):  
Local Rings

scholarly journals Characterizations of regular local rings via syzygy modules of the residue field

2018 ◽  
Vol 10 (3) ◽  
pp. 327-337
Author(s):  
Dipankar Ghosh ◽  
Anjan Gupta ◽  
Tony J. Puthenpurakal
Keyword(s):  
Residue Field ◽  
Local Rings ◽  
Syzygy Modules ◽  
Regular Local Rings

The isomorphisms of orthogonal groups over local rings

1986 ◽  
Vol 2 (4) ◽  
pp. 281-291
Author(s):  
Tang Xiangpu ◽  
An Jianbei
Keyword(s):  
Local Rings ◽  
Orthogonal Groups
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