HOMOMORPHIC IMAGES OF SEMIHEREDITARY RINGS

Authors : Efraim P ARMENDARİZ

Pages : 115-118

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Publication Date : 2009-12-01

Article Type : Research Paper

Abstract :An example is provided of a left semihereditary ring R with an idempotent ideal I such that R/I is not left semihereditary. Two related positive results are provided: a); a left semiartinian, left p.p. ring has nonsingular Loewy factors; b); if R is a commutative von Neumann regular ring and D is an idempotent ideal of R[X] then R[X]/D is semihereditary.
Keywords : semihereditary ring, p p ring, Loewy series, semiartinian