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On Annelidan, Distributive, and Bézout Rings

Abstract

A ring is called right annelidan if the right annihilator of any subset of the ring is comparable with every other right ideal. In this paper we develop the connections between this class of rings and the classes of right Bézout rings and rings whose right ideals form a distributive lattice. We obtain results on localization of right annelidan rings at prime ideals, chain conditions that entail left-right symmetry of the annelidan condition, and construction of completely prime ideals.

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The second author was supported by Polish KBN Grant 1 P03A 032 27. Parts of this paper were written while the first author was visiting the Bialystok University of Technology; other parts were written while the second author was visiting St. Louis University. Each is deeply grateful for the warm hospitality extended by both institutions.

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On Annelidan, Distributive, and Bézout Rings

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