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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Chain type decomposition in integral domains


Author: Raymond A. Beauregard
Journal: Proc. Amer. Math. Soc. 39 (1973), 77-80
MSC: Primary 16A02
DOI: https://doi.org/10.1090/S0002-9939-1973-0314884-2
MathSciNet review: 0314884
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Abstract: Let $ R$ be a (skew) integral domain. For $ 0 \ne a \in R,a$ is simple if the interval $ [aR,R]$ of principal right ideals of $ R$ containing $ aR$ is not the union of two proper subintervals of $ [aR,R]$. It is shown that each irredundant factorization of an element of $ R$ into simple elements is unique up to multiplication by units.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0314884-2
Keywords: Chain of principal right ideals, simple elements, rigid elements, unique factorization
Article copyright: © Copyright 1973 American Mathematical Society