RINGS WHOSE SEMIGROUP OF RIGHT IDEALS IS J -TRIVIAL

Year 2011, Volume: 10 Issue: 10, 151 - 161, 01.12.2011

Henry E. Heatherly Ralph P. Tucci

Abstract

A semigroup S is J -trivial if any two distinct elements of S must
generate distinct ideals of S. We investigate this condition for the semigroup
of all right ideals of a ring under right ideal multiplication. There is a rich interplay
between the underlying ring and the semigroup of all of its right ideals.

Keywords

semigroup of right ideals, ring, J -trivial, idempotents, nilpotent, radicals, π-regular, strongly regular, right weakly regular, 0-cancellative

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• Department of Mathematical Sciences Loyola University New Orleans New Orleans, LA. 70118 e-mail: [e-mail]