Augmentation ideal
id:
augmentation-ideal-242-7434273
title:
Augmentation ideal
text:
In algebra, an augmentation ideal is an ideal that can be defined in any group ring. If G is a group and R a commutative ring, there is a ring homomorphism ε , called the augmentation map, from the group ring R [ G ] to R , defined by taking a (finite) sum ∑ r i g i to ∑ r i . In less formal terms, ε = 1 R for any element g ∈ G , ε = r for any elements r ∈ R and g ∈ G , and ε is then extended to a homomorphism of R-modules in the obvious way. The augmentation ideal A is the kernel of ε and is th
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https://en.wikipedia.org/wiki/Augmentation_ideal
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date modified:
2023-07-18T14:40:08Z
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