The associated graded ring of a group ring

1979 ◽  
pp. 106-129
Author(s):  
Inder Bir S. Passi
Keyword(s):  
Group Ring ◽  
Associated Graded Ring ◽  
Graded Ring

The associated graded ring of an integral group ring

1977 ◽  
Vol 82 (1) ◽  
pp. 25-33 ◽  
Author(s):  
Inder Bir S. Passi ◽  
Lekh Raj Vermani
Keyword(s):  
Abelian Group ◽  
Group Ring ◽  
Symmetric Algebra ◽  
Integral Group Ring ◽  
Augmentation Ideal ◽  
Integral Group ◽  
Finite Abelian Groups ◽  
Associated Graded Ring ◽  
Graded Ring ◽  
Image Position

Let G be an Abelian group, the symmetric algebra of G and the associated graded ring of the integral group ring ZG, where (AG denotes the augmentation ideal of ZG). Then there is a natural epimorphism (4)which is given on the nth component byIn general θ is not an isomorphism. In fact Bachmann and Grünenfelder(1) have shown that for finite Abelian G, θ is an isomorphism if and only if G is cyclic. Thus it is of interest to investigate ker θn for finite Abelian groups. In view of proposition 3.25 of (3) it is enough to consider finite Abelian p-groups.

scholarly journals On the associated graded ring of a group ring

1968 ◽  
Vol 10 (4) ◽  
pp. 411-418 ◽  
Author(s):  
Daniel G Quillen
Keyword(s):  
Group Ring ◽  
Associated Graded Ring ◽  
Graded Ring

On the Buchsbaumness of the Associated Graded Ring of a One-Dimensional Local Ring

2009 ◽  
Vol 37 (5) ◽  
pp. 1594-1603 ◽  
Author(s):  
M. D'Anna ◽  
M. Mezzasalma ◽  
V. Micale
Keyword(s):  
Local Ring ◽  
Associated Graded Ring ◽  
Graded Ring ◽  
One Dimensional
Sign in / Sign up

Export Citation Format

Share Document