Unique factorization monoids and domains
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- by R. E. Johnson PDF
- Proc. Amer. Math. Soc. 28 (1971), 397-404 Request permission
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 $aM \subset bM)$.References
- P. M. Cohn, Factorization in non-commutative power series rings, Proc. Cambridge Philos. Soc. 58 (1962), 452–464. MR 138649, DOI 10.1017/s0305004100036720
- P. M. Cohn, Hereditary local rings, Nagoya Math. J. 27 (1966), 223–230. MR 197498
- Paul Conrad, Generalized semigroup rings, J. Indian Math. Soc. (N.S.) 21 (1957), 73–95 (1958). MR 94369
- L. Fuchs, Partially ordered algebraic systems, Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1963. MR 0171864
- R. E. Johnson, Free products of ordered semigroups, Proc. Amer. Math. Soc. 19 (1968), 697–700. MR 227279, DOI 10.1090/S0002-9939-1968-0227279-5
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 397-404
- MSC: Primary 06.70; Secondary 20.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0277453-7
- MathSciNet review: 0277453