JOURNAL BROWSE
Search
Advanced SearchSearch Tips
OVERRINGS OF THE KRONECKER FUNCTION RING Kr(D, *) OF A PRUFER *-MULTIPLICATION DOMAIN D
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
OVERRINGS OF THE KRONECKER FUNCTION RING Kr(D, *) OF A PRUFER *-MULTIPLICATION DOMAIN D
Chang, Gyu-Whan;
  PDF(new window)
 Abstract
Let * be an e.a.b. star operation on an integrally closed domain D, and let (D, *) be the Kronecker function ring of D. We show that if D is a P*MD, then the mapping is a bijection from the set {} of *-linked overrings of D into the set of overrings of . This is a generalization of [5, Proposition 32.19] that if D is a Prfer domain, then the mapping is a one-to-one mapping from the set {} of overrings of D onto the set of overrings of (D, b).
 Keywords
star operation;Pr *-multiplication domain;Kronecker functionring;*-linked overring;
 Language
English
 Cited by
1.
THE KRONECKER FUNCTION RING OF THE RING D[X]N*,;

대한수학회보, 2010. vol.47. 5, pp.907-913 crossref(new window)
2.
FINITELY t-VALUATIVE DOMAINS,;

Korean Journal of Mathematics, 2014. vol.22. 4, pp.591-598 crossref(new window)
1.
FINITELY t-VALUATIVE DOMAINS, Korean Journal of Mathematics, 2014, 22, 4, 591  crossref(new windwow)
2.
THE KRONECKER FUNCTION RING OF THE RING D[X]N*, Bulletin of the Korean Mathematical Society, 2010, 47, 5, 907  crossref(new windwow)
 References
1.
G. W. Chang, *-Noetherian domains and the ring $D[X]_{N}_*$, J. Algebra 297 (2006), no. 1, 216–233 crossref(new window)

2.
G. W. Chang, Prufer *-multiplication domains, Nagata rings, and Kronecker function rings, J. Algebra 319 (2008), no. 1, 309–319 crossref(new window)

3.
M. Fontana, P. Jara, and E. Santos, Prufer *-multiplication domains and semistar operations, J. Algebra Appl. 2 (2003), no. 1, 21–50 crossref(new window)

4.
M. Fontana and K. A. Loper, An historical overview of Kronecker function rings, Nagata rings, and related star and semistar operations, Multiplicative ideal theory in commutative algebra, 169–187, Springer, New York, 2006 crossref(new window)

5.
R. Gilmer, Multiplicative Ideal Theory, Pure and Applied Mathematics, No. 12. Marcel Dekker, Inc., New York, 1972

6.
E. G. Houston, S. B. Malik, and J. L. Mott, Characterizations of *-multiplication domains, Canad. Math. Bull. 27 (1984), no. 1, 48–52