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The *-Nagata Ring of almost Prüfer *-multiplication Domains
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  • Journal title : Kyungpook mathematical journal
  • Volume 54, Issue 4,  2014, pp.587-593
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2014.54.4.587
 Title & Authors
The *-Nagata Ring of almost Prüfer *-multiplication Domains
Lim, Jung Wook;
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Let D be an integral domain with quotient field K, denote the integral closure of D in K and * be a star-operation on D. In this paper, we study the *-Nagata ring of AP*MDs. More precisely, we show that D is an AP*MD and is a root extension if and only if the *-Nagata ring is an AB-domain, if and only if is an AP-domain. We also prove that D is a P*MD if and only if D is an integrally closed AP*MD, if and only if D is a root closed AP*MD.
*-Nagata ring;almost Prfer *-multiplication domain;Prfer *-multiplication domain;
 Cited by
D. D. Anderson and M. Zafrullah, Almost Bezout domains, J. Algebra, 142(1991), 285-309. crossref(new window)

J. T. Arnold, On the ideal theory of the Kronecker function ring and the domain D(X), Canad. J. Math., 21(1969), 558-563. crossref(new window)

G. W. Chang, H. Kim, and J. W. Lim, Numerical semigroup rings and almost Prufer v-multiplication domains, Comm. Algebra, 40(2012), 2385-2399. crossref(new window)

G. W. Chang and J. W. Lim, Almost Prufer v-multiplication domains and related domains of the form $D+D_S[{\Gamma}^*]$, Comm. Algebra, 41(2013), 2650-2664. crossref(new window)

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

M. Fontana, P. Jara, and E. Santos, Prufer *-multiplication domains and semistar operations, J. Algebra Appl., 2(2003), 21-50. crossref(new window)

R. Gilmer, Commutative Semigroup Rings, The Univ. of Chicago Press, Chicago and London, 1984.

R. Gilmer, Multiplicative Ideal Theory, Queen's Papers in Pure and Appl. Math., vol. 90, Queen's University, Kingston, Ontario, Canada, 1992.

J. Hedstrom and E. Houston, Some remarks on star-operations, J. Pure Appl. Alge bra, 18(1980), 37-44. crossref(new window)

E. G. Houston, S. B. Malik, and J. L. Mott, Characterizations of *-multiplication domains, Canad. Math. Bull., 27(1984), 48-52. crossref(new window)

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

I. Kaplansky, Commutative Rings, Polygonal Publishing House, Washington, New Jersey, 1994.

Q. Li, Almost Prufer *-multiplication domains, Int. J. Algebra, 4(2010), 517-523.

Q. Li, On almost Prufer v-multiplication domains, Algebra Colloq., 19(2012), 493-500. crossref(new window)

A. Mimouni, Note on star operations over polynomial rings, Comm. Algebra, 36(2008), 4249-4256. crossref(new window)