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http://dx.doi.org/10.4134/JKMS.2007.44.4.863

SPECTRAL LOCALIZING SYSTEMS THAT ARE t-SPLITTING MULTIPLICATIVE SETS OF IDEALS  

Chang, Gyu-Whan (DEPARTMENT OF MATHEMATICS UNIVERSITY OF INCHEON)
Publication Information
Journal of the Korean Mathematical Society / v.44, no.4, 2007 , pp. 863-872 More about this Journal
Abstract
Let D be an integral domain with quotient field K, A a nonempty set of height-one maximal t-ideals of D, F$({\Lambda})={I{\subseteq}D|I$ is an ideal of D such that $I{\subseteq}P$ for all $P{\in}A}$, and $D_F({\Lambda})={x{\in}K|xA{\subseteq}D$ for some $A{\in}F({\Lambda})}$. In this paper, we prove that if each $P{\in}A$ is the radical of a finite type v-ideal (resp., a principal ideal), then $D_{F({\Lambda})}$ is a weakly Krull domain (resp., generalized weakly factorial domain) if and only if the intersection $D_{F({\Lambda})}={\cap}_{P{\in}A}D_P$ has finite character, if and only if $F({\Lambda})$ is a t-splitting set of ideals, if and only if $F({\Lambda})$ is v-finite.
Keywords
spectral localizing system; t-splitting set of ideals; weakly Krull domain; generalized weakly factorial domain;
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1 S. Gabelli, On Nagata's theorem for the class group, II, Lecture Notes in Pure and Appl. Math., Vol 206, Marcel Dekker, New York, 1999
2 G. W. Chang, T. Dumitrescu, and M. Zafrullah, t-splitting multiplicative sets of ideals in integral domains, J. Pure Appl. Algebra 197 (2005), no. 1-3, 239-248   DOI   ScienceOn
3 S. El Baghdadi, On a class of Prufer v-multiplication domains, Comm. Algebra 30 (2002), no. 8, 3723-3742   DOI   ScienceOn
4 M. Fontana, J. A. Huckaba, and I. J. Papick, Prufer domains, Marcel Dekker, Inc., New York, 1997
5 E. Houston and M. Zafrullah, On t-invertibility, II, Comm. Algebra 17 (1989), no. 8, 1955-1969   DOI   ScienceOn
6 B. G. Kang, Prufer v-multiplication domains and the ring $R[X]_N_v$, J. Algebra 123 (1989), no. 1, 151-170   DOI
7 I. Kaplansky, Commutative Rings, Revised Ed., The University of Chicago Press, Chicago, Ill.-London, 1974
8 K. A. Loper, A class of Prufer domains that are similar to the ring of entire functions, Rocky Mountain J. Math. 28 (1998), no. 1, 267-285   DOI
9 D. F. Anderson, G. W. Chang, and J. Park, Generalized weakly factorial domains, Houston Math. J. 29 (2003), no. 1, 1-13
10 D. D. Anderson, D. F. Anderson, and M. Zafrullah, The ring $D+XD_S[X]$ and t-splitting sets, Arab. J. Sci. Eng. Sect. C Theme Issues 26 (2001), no. 1, 3-16
11 R. Gilmer and W. Heinzer, Primary ideals with finitely generated radical in a commutative ring, Manuscripta Math. 78 (1993), no. 2, 201-221   DOI
12 D. D. Anderson, J. L. Mott, and M. Zafrullah, Finite character representations for integral domains, Boll. Un. Mat. Ital. B (7) 6 (1992), no. 3, 613-630
13 D. D. Anderson and M. Zafrullah, Weakly factorial domains and groups of divisibility, Proc. Amer. Math. Soc. 109 (1990), no. 4, 907-913   DOI   ScienceOn
14 R. Gilmer, Multiplicative Ideal Theory, Marcel Dekker, New York, 1972
15 J. T. Arnold and J. W. Brewer, On flat overrings, ideal transforms and generalized transforms of a commutative ring, J. Algebra 18 (1971), 254-263   DOI
16 G. W. Chang, Weakly factorial rings with zero divisors, Lecture Notes in Pure and Appl. Math., 220, Dekker, New York, 2001
17 G. W. Chang, T. Dumitrescu, and M. Zafrullah, t-splitting sets in integral domains, J. Pure Appl. Algebra 187 (2004), no. 1-3, 71-86   DOI   ScienceOn