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Let D be an integrally closed domain with quotient field K,* be a star operation on D, X, Y be indeterminates over D, N* = {f ∈D[X]| (cD(f))* = D} and R = D[X]N* . Let b be the b-operation on R,and let *c be the star operation on D defined by I*c = (ID[X]N* )b ∩K.
Finally, let Kr(R, b) (resp., Kr(D, *c)) 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, *c) 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, *c) if and only if D is a P*MD. As a corollary, we have that if D is not a P*MD, 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.
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참고문헌 (10)
참고문헌 신청
B. G. Kang / 1989 / Prufer v-multiplication domains and the ring R[X]Nv / J. Algebra 123 (1) : 151 ~ 170
D. D. Anderson / 1977 / Some remarks on the ring R(X) / Comment. Math. Univ. St. Paul. 26 (2) : 137 ~ 140
D. F. Anderson / 1990 / Characterizing Kronecker function rings / Ann. Univ. Ferrara Sez. VII (N.S.) 36 : 1 ~ 13
E. G. Houston / 1984 / Characterizations of *-multiplication domains / Canad. Math. Bull. 27 (1) : 48 ~ 52
G. W. Chang / 2003 / Star-invertible ideals of integral domains / Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. 6 (1) : 141 ~ 150
D. D. Anderson / 1977 / Some remarks on the ring R(X) / Comment. Math. Univ. St. Paul. 26 (2) : 137 ~ 140
D. F. Anderson / 1990 / Characterizing Kronecker function rings / Ann. Univ. Ferrara Sez. VII (N.S.) 36 : 1 ~ 13
E. G. Houston / 1984 / Characterizations of *-multiplication domains / Canad. Math. Bull. 27 (1) : 48 ~ 52
G. W. Chang / 2003 / Star-invertible ideals of integral domains / Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. 6 (1) : 141 ~ 150
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