Right $\textrm {LCM}$ domains
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- by Raymond A. Beauregard PDF
- Proc. Amer. Math. Soc. 30 (1971), 1-7 Request permission
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.References
- Raymond A. Beauregard, Infinite primes and unique factorization in a principal right ideal domain, Trans. Amer. Math. Soc. 141 (1969), 245–253. MR 242879, DOI 10.1090/S0002-9947-1969-0242879-X
- P. M. Cohn, Noncommutative unique factorization domains, Trans. Amer. Math. Soc. 109 (1963), 313–331. MR 155851, DOI 10.1090/S0002-9947-1963-0155851-X
- Nathan Jacobson, The Theory of Rings, American Mathematical Society Mathematical Surveys, Vol. II, American Mathematical Society, New York, 1943. MR 0008601, DOI 10.1090/surv/002
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 1-7
- MSC: Primary 16.15
- DOI: https://doi.org/10.1090/S0002-9939-1971-0279125-1
- MathSciNet review: 0279125