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Factorization in integral domains. II. (English) Zbl 0776.13001

Les AA. continuent l’étude des propriétés des anneaux intègres, qui sont plus faibles que les propriétés de anneaux factoriels, commencé dans la première partie du papier [cf. J. Pure Appl. Algebra 69, No. 1, 1-19 (1990; Zbl 0727.13007)]. Dans cette deuxième partie sont étudiés les comportements des propriétés pour les extensions d’anneaux intègres: localisations, en particulier par un système multiplicatif engendré par des éléments primes, et pour les réunions filtrantes d’anneaux.

MSC:

13A05 Divisibility and factorizations in commutative rings
13G05 Integral domains
13F99 Arithmetic rings and other special commutative rings

Citations:

Zbl 0727.13007
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References:

[1] Anderson, D. D.; Anderson, D. F.; Zafrullah, M., Factorization in integral domains, J. Pure Appl. Algebra, 69, 1-19 (1990) · Zbl 0727.13007
[2] Anderson, D. D.; Anderson, D. F.; Zafrullah, M., Rings between \(D[X]\) and \(K[X]\), Houston Math. J., 17, 109-129 (1991) · Zbl 0736.13015
[3] Anderson, D. F., Integrally closed domains, Comment. Math. Univ. St. Paul., 32, 37-38 (1983) · Zbl 0521.13002
[4] Brandis, A., Über die multiplikative Struktur von Körpererweiterungen, Math. Z., 87, 71-73 (1965) · Zbl 0127.26304
[5] Cohn, P. M., Bézout rings and their subrings, (Proc. Cambridge Philos. Soc., 64 (1968)), 251-264 · Zbl 0157.08401
[6] Cohn, P. M., Unique factorization domains, Amer. Math. Monthly, 80, 1-18 (1973) · Zbl 0256.13011
[7] Fossum, R. M., The Divisor Class Group of a Krull Domain (1973), Springer-Verlag: Springer-Verlag New York · Zbl 0256.13001
[8] Gabelli, S.; Roitman, M., On Nagata’s theorem for the class group, J. Pure Appl. Algebra, 66, 31-42 (1990) · Zbl 0717.13010
[9] Gilmer, R., Multiplicative Ideal Theory (1972), Dekker: Dekker New York · Zbl 0248.13001
[10] Gilmer, R.; Parker, T., Divisibility properties in semigroup rings, Michigan Math. J., 21, 65-86 (1974) · Zbl 0285.13007
[11] Grams, A., Atomic domains and the ascending chain condition for principal ideals, (Proc. Cambridge Philos. Soc., 75 (1974)), 321-329 · Zbl 0287.13002
[12] Grams, A.; Warner, H., Irreducible divisors in domains of finite character, Duke Math. J., 42, 271-284 (1975) · Zbl 0349.13006
[13] Kaplansky, I., Commutative Rings (1974), Univ. of Chicago Press: Univ. of Chicago Press Chicago · Zbl 0203.34601
[14] Mott, J. L.; Schexnayder, M., Exact sequences of semi-value groups, J. Reine Angew. Math., 283/284, 388-401 (1976) · Zbl 0347.13001
[15] Nagata, M., A remark on the unique factorization theorem, J. Math. Soc. Japan, 9, 143-145 (1957) · Zbl 0079.05405
[16] Roitman, M., On Mori domains and commutative rings with \(CC^⊥I\), J. Pure Appl. Algebra, 56, 247-268 (1988) · Zbl 0677.13005
[17] Zaks, A., Half-factorial domains, Bull. Amer. Math. Soc., 82, 721-724 (1976) · Zbl 0338.13020
[18] Zaks, A., Half-factorial domains, Israel J. Math., 37, 281-302 (1980) · Zbl 0509.13017
[19] Zaks, A., Atomic rings without a.c.c. on principal ideals, J. Algebra, 74, 223-231 (1982) · Zbl 0484.13012
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