Primary factorization in a weak Bezout domain
Authors:
R. A. Beauregard and R. E. Johnson
Journal:
Proc. Amer. Math. Soc. 25 (1970), 662-665
MSC:
Primary 16.15
DOI:
https://doi.org/10.1090/S0002-9939-1970-0262274-0
MathSciNet review:
0262274
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Abstract | References | Similar Articles | Additional Information
Abstract: It is well known that in a weak Bezout domain each prime factorization of an element is unique up to similarity. In this paper, a corresponding extension to primary factorizations is obtained.
- 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 https://doi.org/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 https://doi.org/10.1090/S0002-9947-1963-0155851-X
- P. M. Cohn, Bezout rings and their subrings, Proc. Cambridge Philos. Soc. 64 (1968), 251–264. MR 222065, DOI https://doi.org/10.1017/s0305004100042791
- R. E. Williams, A note on weak Bezout rings, Proc. Amer. Math. Soc. 19 (1968), 951–952. MR 228528, DOI https://doi.org/10.1090/S0002-9939-1968-0228528-X
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Keywords:
Weak Bezout domain,
unique prime factorization,
unique primary factorization
Article copyright:
© Copyright 1970
American Mathematical Society