Vol. 47, No. 2, 1973

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One sided prime ideals

John Dauns

Vol. 47 (1973), No. 2, 401–412
Abstract

Consider a right ideal L in a ring (with 1 R or 1R), its idealizer N = {n R|nL L}, the bound P = {r L|Rr L} ⊲ R of L, and the ideal H = {n N|nL P} ⊲ N. II. Some of the ideal structure of the ring N∕P is determined for a class of one sided prime ideals L more general than the almost maximal ones and without any chain conditions on R (Theorem II). III. When LP the following conditions are necessary and sufficient for N∕P to have precisely two unequal, nonzero minimal prime ideals L∕P and H∕P: (i) HP; (ii) L∕P < R∕P is not essential; (iii) L∕P is a maximal annihilator in R∕P; (iv) the left annihilator of L∕P is not zero; (v) L = {r R|ur P} for some u NL (Theorem III).

Mathematical Subject Classification
Primary: 16A66
Milestones
Received: 8 May 1972
Revised: 3 February 1973
Published: 1 August 1973
Authors
John Dauns