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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Right $ {\rm LCM}$ domains


Author: Raymond A. Beauregard
Journal: Proc. Amer. Math. Soc. 30 (1971), 1-7
MSC: Primary 16.15
MathSciNet review: 0279125
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Abstract: A right LCM domain is a not necessarily commutative integral domain with unity in which the intersection of any two principal right ideals is again principal. The principal result deals with right LCM domains that satisfy an additional mild hypothesis; for such rings (which include right HCF domains and weak Bezout domains) it is shown that each prime factorization of an element is unique up to order of factors and projective factors. Projectivity is an equivalence relation that reduces to the relation of ``being associates'' in commutative rings and reduces to similarity in weak Bezout domains.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0279125-1
PII: S 0002-9939(1971)0279125-1
Keywords: Right LCM domain, right HCF domain, weak Bezout domain, unique prime factorization
Article copyright: © Copyright 1971 American Mathematical Society