On rings whose Jacobson radical coincides with upper nilradical

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The Upper Nilradical and Jacobson Radical of Semigroup Graded Rings

Given a semigroup S, we prove that if the upper nilradical Nil∗(R) is homogeneous whenever R is an S-graded ring, then the semigroup S must be cancelative and torsion-free. In case S is commutative the converse is true. Analogs of these results are established for other radicals and ideals. We also describe a large class of semigroups S with the property that whenever R is a Jacobson radical ri...

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ژورنال

عنوان ژورنال: TURKISH JOURNAL OF MATHEMATICS

سال: 2021

ISSN: 1303-6149

DOI: 10.3906/mat-2012-30