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Right Invariant Right Hereditary Rings

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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Let R be a right hereditary domain in which all right ideals are two-sided (i.e., R is right invariant). We show that R is the intersection of generalized discrete valuation rings and that every right ideal is the product of prime ideals. This class of rings seems comparable with (and contains) the class of commutative Dedekind domains, but the rings considered here are in general not maximal orders and not Dedekind rings in the terminology of Robson [9]. The left order of a right ideal of such a ring is a ring of the same kind and the class contains right principal ideal domains in which the maximal right ideals are two-sided [6].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 5 , October 1974 , pp. 1186 - 1191
Copyright
Copyright © Canadian Mathematical Society 1974

References

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