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POWER SERIES RINGS OVER PRÜFER v-MULTIPLICATION DOMAINS
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 Title & Authors
POWER SERIES RINGS OVER PRÜFER v-MULTIPLICATION DOMAINS
Chang, Gyu Whan;
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 Abstract
Let D be an integral domain, {} be a nonempty set of indeterminates over D, and be the first type power series ring over D. We show that if D is a t-SFT v-multiplication domain, then is a Krull domain, and is a v-multiplication domain if and only if D is a Krull domain.
 Keywords
t-operation;t-SFT PvMD;power series ring;Krull domain;
 Language
English
 Cited by
 References
1.
D. D. Anderson, B. G. Kang, and M. H. Park, Anti-Archimedean rings and power series rings, Comm. Algebra 26 (1998), 3223-3238. crossref(new window)

2.
D. D. Anderson and M. Zafrullah, Almost Bezout domains, J. Algebra 142 (1991), 285-309. crossref(new window)

3.
J. Arnold, Power series rings over Prufer domains, Pacific J. Math. 44 (1973), 1-11. crossref(new window)

4.
J. Arnold, Power series rings with finite Krull dimension, Indiana Univ. Math. J. 31 (1982), 897-911. crossref(new window)

5.
G. W. Chang, A pinched-Krull domain at a prime ideal, Comm. Algebra 30 (2002), 3669-3686. crossref(new window)

6.
G. W. Chang, Spectral localizing systems that are t-splitting multiplicative sets of ideals, J. Korean Math. Soc. 44 (2007), 863-872. crossref(new window)

7.
G. W. Chang and M. Fontana, Upper to zero in polynomial rings and Prufer-like domains, Comm. Algebra 37 (2009), 164-192. crossref(new window)

8.
G. W. Chang and D. Y. Oh, The rings $D((X))_i$ and D{{X}}$_i$, J. Algebra Appl. 12 (2013), 1250147 (11 pages).

9.
D. Dobbs, E. Houston, T. Lucas, and M. Zafrullah, t-linked overrings and Prufer vmultiplication domains, Comm. Algebra 17 (1989), 2835-2852. crossref(new window)

10.
M. Fontana and S. Gabelli, On the class group and the local class group of a pullback, J. Algebra 181 (1996), 803-835. crossref(new window)

11.
M. Fontana, S. Gabelli, and E. Houston, UMT-domains and domains with Prufer integral closure, Comm. Algebra 26 (1998), 1017-1039. crossref(new window)

12.
R. Gilmer, Power series rings over a Krull domain, Pacific J. Math. 29 (1969), 543-549. crossref(new window)

13.
R. Gilmer, Multiplicative Ideal Theory, Marcel Dekker, New York, 1972.

14.
R. Gilmer and W. Heinzer, Primary ideals with finitely generated radical in a commutative ring, Manuscripta Math. 78 (1993), 201-221. crossref(new window)

15.
E. Houston and M. Zafrullah, On t-invertibility II, Comm. Algebra 17 (1989), 1955-1969. crossref(new window)

16.
B. G. Kang, Prufer v-multiplication domains and the ring $R[X]_{N_v}$, J. Algebra 123 (1989), 151-170. crossref(new window)

17.
B. G. Kang and M. H. Park, A note on t-SFT-rings, Comm. Algebra 34 (2006), 3153-3165. crossref(new window)

18.
D. J. Kwak and Y. S. Park, On t-flat overrings, Chinese J. Math. 23 (1995), 17-24.

19.
J. Mott and M. Zafrullah, On Krull domains, Arch. Math. 56 (1991), 559-568. crossref(new window)