RINGS WHOSE SEMIGROUP OF RIGHT IDEALS IS J -TRIVIAL

Authors : Henry E Heatherly, Ralph P Tucci

Pages : 151-161

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Publication Date : 2011-12-01

Article Type : Research Paper

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