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Bezout Domains and Rings with a Distributive Lattice of Right Ideals

Published online by Cambridge University Press:  20 November 2018

H. H. Brungs
H. H. Brungs*
Affiliation:
University of Alberta, Edmonton, Alberta
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It is the purpose of this paper to discuss a construction of right arithmetical (or right D-domains in [5]) domains, i.e., integral domains R for which the lattice of right ideals is distributive (see also [3]). Whereas the commutative rings in this class are precisely the Prüfer domains, not even right and left principal ideal domains are necessarily arithmetical. Among other things we show that a Bezout domain is right arithmetical if and only if all maximal right ideals are two-sided.

Any right ideal of a right noetherian, right arithmetical domain is two-sided. This fact makes it possible to describe the semigroup of right ideals in such a ring in a satisfactory way; [3], [5].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 2 , 01 April 1986 , pp. 286 - 303
Copyright
Copyright © Canadian Mathematical Society 1986

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