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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: 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.


References [Enhancements On Off] (What's this?)

  • [1] R. A. Beauregard, Infinite primes and unique factorization in a principal right ideal domain, Trans. Amer. Math. Soc. 141 (1969), 245-254. MR 0242879 (39:4206)
  • [2] P. M. Cohn, Noncommutative unique factorization domains, Trans. Amer. Math. Soc. 109 (1963), 313-331. MR 27 #5785. MR 0155851 (27:5785)
  • [3] -, Bezout rings and their subrings, Proc. Cambridge Philos. Soc. 64 (1968), 251-264. MR 36 #5117. MR 0222065 (36:5117)
  • [4] R. E. Williams, A note on weak Bezout rings, Proc. Amer. Math. Soc. 19 (1968), 951-952. MR 37 #4108. MR 0228528 (37:4108)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0262274-0
Keywords: Weak Bezout domain, unique prime factorization, unique primary factorization
Article copyright: © Copyright 1970 American Mathematical Society

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