RINGS WHOSE SEMIGROUP OF RIGHT IDEALS IS J -TRIVIAL

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