KRONECKER FUNCTION RINGS AND PRUFER-LIKE DOMAINS
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Let D be an integral domain, D be the integral closure of D, * be a star operation of nite character on D, *w be the so-called *w-operation on D induced by *, X be an indeterminate over D, N* = ff 2 D[X]jc(f)* = Dg, and Kr(D; ) =f0g [ ff g j0 6= f; g 2 D[X] and there is an 0 6= h 2 D[X] such that (c(f)c(h))* (c(g)c(h))*g. In this paper, we show that D is a *-quasi-Prufer domain if and only if D [X]N* = Kr(D; *w). As a corollary, we recover Fontana-Jara-Santos's result that D is a Prufer *-multiplication domain if and only if D[X]N* = Kr(D; *w).
Abstract
Let D be an integral domain, D be the integral closure of D, * be a star operation of nite character on D, *w be the so-called *w-operation on D induced by *, X be an indeterminate over D, N* = ff 2 D[X]jc(f)* = Dg, and Kr(D; ) =f0g [ ff g j0 6= f; g 2 D[X] and there is an 0 6= h 2 D[X] such that (c(f)c(h))* (c(g)c(h))*g. In this paper, we show that D is a *-quasi-Prufer domain if and only if D [X]N* = Kr(D; *w). As a corollary, we recover Fontana-Jara-Santos's result that D is a Prufer *-multiplication domain if and only if D[X]N* = Kr(D; *w).
참고문헌 (17)
- D.D. Anderson, "Two star operations and their induced lattices", Comm. Algebra, 28, pp.2461~2475 (2000)
- J.T. Arnold, "On the ideal theory of the Kronecker function ring and the domain D(X)", Canad. J. Math, 21, pp.558~563 (1969)
- N, "J. Algebra", 2006, 216~233
- G.W. Chang, "Prufer -multiplication domains, Nagata rings, and Kronecker function rings", J. Algebra, 319, pp.309~319 (2008)
- G.W. Chang, "Upper to zero in polynomial rings and Prufer-like domains", Comm. Algebra, 37, pp.164~192 (2009)
- G.W. Chang, "The w-integral closure of integral domains", J. Algebra, 259, pp.195~210 (2006)
- M. Fontana, "UMT-domains and domains with Prufer integral closure", Comm. Algebra, 26, pp.1017~1039 (1998)
- M. Fontana, "Prufer domains" (1997), Marcel Dekker
- M. Fontana, "Prufer -multiplication domains and semis- tar operations", J. Algebra Appl, 2, pp.1~30 (2003)
- M. Fontana, "Kronecker function rings: a general approach, in Ideal Theoretic Methods in Commutative Algebra", pp.189~205 (2001), Marcel Dekker
- M. Fontana, "Nagata rings, Kronecker function rings and related semistar operations", Comm. Algebra, 31, pp.4775~4801 (2003)
- M. Fontana, "A historical overview of Kronecker function rings, Nagata rings, and related star and semistar operations, In Multiplicative Ideal Theory in Commutative Algebra", pp.169~187 (2006), Springer
- R. Gilmer, "Multiplicative Ideal Theory" (1972), Dekker
- E. Houston, "Characterizations of -multiplication do- mains", Canad. Math. Bull, 27, pp.48~52 (1984)
- E. Houston, "On t-invertibility, II", Comm. Algebra, 17, pp.1955~1969 (1989)
- Nv, "J. Algebra", 1989, 151~170
- A. Okabe, "Star operations and generalized integral closures", Bull. Fac. Sci., Ibaraki Univ, 24, pp.7~13 (1992)