Geodesic
An Analog of Nagata's Theorem for Modular LCM Domains
Canadian journal of mathematics, Tome 29 (1977) no. 2, pp. 307-314

Voir la notice de l'article provenant de la source Cambridge University Press

The theorem referred to in the title asserts that for an atomic commutative integral domain R, if S is a submonoid of R* (the monoid of nonzero elements of R) generated by primes such that the quotient ring RS-1 is a UFD (unique factorization domain) then R is also a UFD [8]. Recently several definitions of a noncommutative UFD have been proposed (see the summary in [6]). 
Beauregard, Raymond A. An Analog of Nagata's Theorem for Modular LCM Domains. Canadian journal of mathematics, Tome 29 (1977) no. 2, pp. 307-314. doi: 10.4153/CJM-1977-034-6
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[1] 1. Beauregard, R. A., Right LCM domains, Proc. Amer. Math. Soc. 30 (1971), 1–7. Google Scholar

[2] 2. Beauregard, R. A. Right quotient rings of a right LCM domain, Can. J. Math. 24 (1972), 983–988. Google Scholar

[3] 3. Beauregard, R. A. Right bounded factors in an LCM domain, Trans. Amer. Math. Soc. 200 (1974), 251–266. Google Scholar

[4] 4. Brungs, H. H., Ringe mit eindeutiger Factorzerlegung, J. Reine Angew. Math. 236 (1969), 43–66. Google Scholar

[5] 5. Cohn, P. M., Noncommutative unique factorization domains, Trans. Amer. Math. Soc. 109 (1963), 313–331. Google Scholar

[6] 6. Cohn, P. M. Unique factorization domains, Amer. Math. Monthly 80 (1973), 1–18. Google Scholar

[7] 7. Gilmer, R. and Parker, T., Divisibility properties in semigroup rings, Michigan Math. J. 21 (1974), 65–86. Google Scholar

[8] 8. Nagata, M., A remark on the unique factorization theorem, J. Math. Soc. Japan 9 (1957), 143–145. Google Scholar

[9] 9. Samuel, P., On unique factorization domains, 111. J. Math. 5 (1961), 1–17. Google Scholar

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