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Let D be an integral domain with quotient field K, X be a nonempty set of indeterminates over D, * be a star operation on D,N_* = <수식>, *w be the star operation on D defined by I*w = <수식>, and [*] be the star operation on D[X] canonically associated to * as in Theorem 2.1. Let A^g (resp., A^*g, A^([*]g)) be the global (resp., *-global, [*]-global) transform of a ring A. We show that D is a *w-Noetherian domain if and only if D[X] is a [*]-Noetherian domain.
We prove that D^(*g)[X]_(N*) = (D[X]_N* )^g = (D[X])[*]g; hence if D is a *w-Noetherian domain, then each ring between D[X]_(N*) and D^(*g)[X]_(N*)is a Noetherian domain. Let D = <수식> and ht P ≥ 2.
We show that <수식> and study some properties of D and D^(*g).
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참고문헌 (20)
참고문헌 신청
A. R. Wadsworth / 1974 / Pairs of domains where all intermediate domains are Noetherian / Trans. Amer. Math. Soc 195 : 201 ~ 211
B. G. Kang / 1989 / Prufer v-multiplication domains and the ring R[X]Nv / J. Algebra 123 (1) : 151 ~ 170
D. D. Anderson / 1980 / Global transforms and Noetherian pairs / Hiroshima Math. J 10 (1) : 69 ~ 74
D. D. Anderson / 2000 / Two star-operations and their induced lattices / Comm. Algebra 28 (5) : 2461 ~ 2475
D. Dobbs / 1989 / t-linked overrings and Prufer v- multiplication domains / Comm. Algebra 17 (11) : 2835 ~ 2852
B. G. Kang / 1989 / Prufer v-multiplication domains and the ring R[X]Nv / J. Algebra 123 (1) : 151 ~ 170
D. D. Anderson / 1980 / Global transforms and Noetherian pairs / Hiroshima Math. J 10 (1) : 69 ~ 74
D. D. Anderson / 2000 / Two star-operations and their induced lattices / Comm. Algebra 28 (5) : 2461 ~ 2475
D. Dobbs / 1989 / t-linked overrings and Prufer v- multiplication domains / Comm. Algebra 17 (11) : 2835 ~ 2852
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