A characterization of general $\textrm {Z}.\textrm {P}.\textrm {I}.$-rings
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- by Kathleen B. Levitz PDF
- Proc. Amer. Math. Soc. 32 (1972), 376-380 Request permission
Abstract:
A commutative ring A is a general Z.P.I.-ring if each ideal of A can be represented as a finite product of prime ideals. We prove that a commutative ring A is a general Z.P.I.-ring if each finitely generated ideal of A can be represented as a finite product of prime ideals. We also give a characterization of Krull domains in terms of $^ \ast$-operations, as defined by Gilmer.References
- Tomoharu Akiba, Remarks on generalized rings of quotients, Proc. Japan Acad. 40 (1964), 801–806. MR 180573
- Robert W. Gilmer, Multiplicative ideal theory, Queen’s Papers in Pure and Applied Mathematics, No. 12, Queen’s University, Kingston, Ont., 1968. MR 0229624
- Robert W. Gilmer, Multiplicative ideal theory, Queen’s Papers in Pure and Applied Mathematics, No. 12, Queen’s University, Kingston, Ont., 1968. MR 0229624
- Shinziro Mori, Über die Produktzerlegung der Hauptideale. III, J. Sci. Hiroshima Univ. Ser. A 10 (1940), 85–94 (German). MR 1965
- Shinziro Mori, Über die Produktzerlegung der Hauptideale. IV, J. Sci. Hiroshima Univ. Ser. A 11 (1941), 7–14 (German). MR 4230
- Shinziro Mori, Allgemeine Z.P.I.-Ringe, J. Sci. Hiroshima Univ. Ser. A 10 (1940), 117–136. MR 2847
- Toshio Nishimura, Unique factorization of ideals in the sense of quasi-equality, J. Math. Kyoto Univ. 3 (1963), 115–125. MR 156866, DOI 10.1215/kjm/1250524862 S. Tramel, Factorization of principal ideals in the sense of quasi-equality, Doctoral Dissertation, Louisiana State University, Baton Rouge, La., 1968.
- Craig A. Wood, On general $\textrm {Z.P.I.}$-rings, Pacific J. Math. 30 (1969), 837–846. MR 248126 —, On general Z.P.I.-rings, Doctoral Dissertation, Florida State University, Tallahassee, Fla., 1967.
- Oscar Zariski and Pierre Samuel, Commutative algebra, Volume I, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, New Jersey, 1958. With the cooperation of I. S. Cohen. MR 0090581
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 376-380
- MSC: Primary 13A15
- DOI: https://doi.org/10.1090/S0002-9939-1972-0294312-5
- MathSciNet review: 0294312