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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).
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참고문헌 (17)
참고문헌 신청
A. Okabe / 1992 / Star operations and generalized integral closures / Bull. Fac. Sci., Ibaraki Univ 24 : 7 ~ 13
B.G. Kang / 1989 / Prufer v-multiplication domains and the ring R[X]Nv / J. Algebra 123 : 151 ~ 170
D.D. Anderson / 2000 / Two star operations and their induced lattices / Comm. Algebra 28 : 2461 ~ 2475
E. Houston / 1984 / Characterizations of -multiplication do- mains / Canad. Math. Bull 27 : 48 ~ 52
E. Houston / 1989 / On t-invertibility, II / Comm. Algebra 17 : 1955 ~ 1969
B.G. Kang / 1989 / Prufer v-multiplication domains and the ring R[X]Nv / J. Algebra 123 : 151 ~ 170
D.D. Anderson / 2000 / Two star operations and their induced lattices / Comm. Algebra 28 : 2461 ~ 2475
E. Houston / 1984 / Characterizations of -multiplication do- mains / Canad. Math. Bull 27 : 48 ~ 52
E. Houston / 1989 / On t-invertibility, II / Comm. Algebra 17 : 1955 ~ 1969
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