Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897530 | Journal of Pure and Applied Algebra | 2018 | 16 Pages |
Abstract
In this paper we study the homogeneity of radicals defined by nilpotence or primality conditions, in rings graded by a semigroup S. When S is a unique product semigroup, we show that the right (and left) strongly prime and uniformly strongly prime radicals are homogeneous, and an even stronger result holds for the generalized nilradical. We further prove that rings graded by torsion-free, nilpotent groups have homogeneous upper nilradical. We conclude by showing that non-semiprime rings graded by a large class of semigroups must always contain nonzero homogeneous nilpotent ideals.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Chan Yong Hong, Nam Kyun Kim, Blake W. Madill, Pace P. Nielsen, MichaÅ Ziembowski,