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THE KRONECKER FUNCTION RING OF THE RING D[X]N*
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 Title & Authors
THE KRONECKER FUNCTION RING OF THE RING D[X]N*
Chang, Gyu-Whan;
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 Abstract
Let D be an integrally closed domain with quotient field K, * be a star operation on D, X, Y be indeterminates over D, and . Let b be the b-operation on R, and let be the star operation on D defined by . Finally, let Kr(R, b) (resp., Kr(D, )) be the Kronecker function ring of R (resp., D) with respect to Y (resp., X, Y). In this paper, we show that Kr(R, b) Kr(D, ) and Kr(R, b) is a kfr with respect to K(Y) and X in the notion of [2]. We also prove that Kr(R, b) = Kr(D, ) if and only if D is a . As a corollary, we have that if D is not a , then Kr(R, b) is an example of a kfr with respect to K(Y) and X but not a Kronecker function ring with respect to K(Y) and X.
 Keywords
(e.a.b.) star operation;Kronecker function ring (KFR);kfr;Nagata ring;P*MD;
 Language
English
 Cited by
1.
Topological properties of semigroup primes of a commutative ring, Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2017, 58, 3, 453  crossref(new windwow)
 References
1.
D. D. Anderson, Some remarks on the ring R(X), Comment. Math. Univ. St. Paul. 26 (1977/78), no. 2, 137-140.

2.
D. F. Anderson, D. E. Dobbs, and M. Fontana, Characterizing Kronecker function rings, Ann. Univ. Ferrara Sez. VII (N.S.) 36 (1990), 1-13.

3.
G. W. Chang, $\ast$-Noetherian domains and the ring $D[X]_{N_{\ast}}$, J. Algebra 297 (2006), no. 1, 216-233. crossref(new window)

4.
G. W. Chang, Prufer *-multiplication domains, Nagata rings, and Kronecker function rings, J. Algebra 319 (2008), no. 1, 309-319. crossref(new window)

5.
G. W. Chang, Overrings of the Kronecker function ring Kr(D,*) of a Prufer *-multiplication domain D, Bull. Korean Math. Soc. 46 (2009), no. 5, 1013-1018. crossref(new window)

6.
G. W. Chang and J. Park, Star-invertible ideals of integral domains, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 6 (2003), no. 1, 141-150.

7.
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.

8.
R. Gilmer, Multiplicative Ideal Theory, Marcel Dekker, Inc., New York, 1972.

9.
E. G. Houston, S. B. Malik, and J. L. Mott, Characterizations of $^*$-multiplication domains, Canad. Math. Bull. 27 (1984), no. 1, 48-52. crossref(new window)

10.
B. G. Kang, Prufer v-multiplication domains and the ring $R[X]_{N_v}$, J. Algebra 123 (1989), no. 1, 151-170. crossref(new window)