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Original Articles

On graded Thierrin radicals of graded rings

Pages 3886-3891 | Received 10 Sep 2016, Published online: 31 Jan 2017
 

ABSTRACT

In this paper, we study the graded Thierrin radical and the classical Thierrin radical of a graded ring, which is the direct sum of a family of its additive subgroups indexed by a nonempty set, under the assumption that the product of homogeneous elements is again homogeneous. There are two versions of this graded radical, the graded Thierrin and the large graded Thierrin radical. We establish several characterizations of the graded Thierrin radical and prove that the largest homogeneous ideal contained in the classical Thierrin radical of a graded ring coincides with the large graded Thierrin radical of that ring.

2010 MATHEMATICS SUBJECT CLASSIFICATION:

Acknowledgments

I would like to express my gratitude to the referee for a careful reading of the article.

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