Chain type decomposition in integral domains
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- by Raymond A. Beauregard PDF
- Proc. Amer. Math. Soc. 39 (1973), 77-80 Request permission
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.References
- P. M. Cohn, Factorization in general rings and strictly cyclic modules, J. Reine Angew. Math. 239(240) (1969), 185–200. MR 257121, DOI 10.1515/crll.1969.239-240.185
- R. E. Johnson, Unique factorization in a principal right ideal domain, Proc. Amer. Math. Soc. 16 (1965), 526–528. MR 175927, DOI 10.1090/S0002-9939-1965-0175927-8
- R. E. Johnson, Unique factorization monoids and domains, Proc. Amer. Math. Soc. 28 (1971), 397–404. MR 277453, DOI 10.1090/S0002-9939-1971-0277453-7
Additional Information
- © Copyright 1973 American Mathematical Society
- 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