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

Unique factorization monoids and domains


Author: R. E. Johnson
Journal: Proc. Amer. Math. Soc. 28 (1971), 397-404
MSC: Primary 06.70; Secondary 20.00
MathSciNet review: 0277453
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Abstract: It is the purpose of this paper to construct unique factorization (uf) monoids and domains. The principal results are: (1) The free product of a well-ordered set of monoids is a uf-monoid iff every monoid in the set is a uf-monoid. (2) If $ M$ is an ordered monoid and $ F$ is a field, the ring $ F[[M]]$ of all formal power series with well-ordered support is a uf-domain iff $ M$ is naturally ordered (i.e., whenever $ b < a$ and $ aM{ \bigcap ^b}M \ne \emptyset $, then $ aM \subset bM)$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0277453-7
PII: S 0002-9939(1971)0277453-7
Keywords: Free products of monoids, unique factorization monoids, unique factorization domains, noncommutative power series rings
Article copyright: © Copyright 1971 American Mathematical Society