Journal article
π-domains, overrings, and divisorial ideals
Glasgow Mathematical Journal, Vol.19(2), pp.199-203
1978
DOI: 10.1017/S001708950000361X
Abstract
In this paper we study several generalizations of the concept of unique factorization domain. An integral domain is called a π-domain if every principal ideal is a product of prime ideals. Theorem 1 shows that the class of π-domains forms a rather natural subclass of the class of Krull domains. In Section 3 we consider overrings of π-domains. In Section 4 generalized GCD-domains are introduced: these form an interesting class of domains containing all Prüfer domains and all π-domains. © 1978, Glasgow Mathematical Journal Trust. All rights reserved.
Details
- Title: Subtitle
- π-domains, overrings, and divisorial ideals
- Creators
- D.D. Anderson - University of Missouri
- Resource Type
- Journal article
- Publication Details
- Glasgow Mathematical Journal, Vol.19(2), pp.199-203
- DOI
- 10.1017/S001708950000361X
- ISSN
- 0017-0895
- Comment
- References: Arnold, J.T., Brewer, J.W., On flat overrings, ideal transforms and generalized transforms of a commutative ring (1971) J. Algebra, 18, pp. 254-263; Bourbaki, N., (1972) Commutative Algebra, , Addison-Wesley; Claborn, L., Every abelian group is a class group (1966) Pacific J. Math., 18, pp. 219-222; Claborn, L., A note on the class group (1966) Pacific J. Math., 18, pp. 223-225; Fossum, R.M., (1973) The Divisor Class Group of a Krull Domain, , Springer; Gilmer, R., (1972) Multiplicative Ideal Theory, , Dekker; Kaplansky, I., (1974) Commutative Rings, , University of Chicago Press; Krull, W., Zur Arithmetik der endlichen diskreten Hauptordnungen (1951) J. Reine Angew. Math., 189, pp. 118-128; Levitz, K.B., A characterization of general Z.P.I.-rings (1972) Proc. Amer. Math. Soc., 32, pp. 376-380; Sheldon, P., Prime ideals in a GCD-domain (1974) Canad. J. Math., 26, pp. 98-107; Storch, U., (1967) Fastfaktorielle Ringe, , Schriftenreihe Math. Inst. Univ. Munster, Heft 36. Max Kramer
- Language
- English
- Date published
- 1978
- Academic Unit
- Mathematics
- Record Identifier
- 9984230625402771
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