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초록· 키워드
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Let D be an integral domain, P be a nonzero prime ideal of D,
{Pα｜α∈A} be a nonempty set of prime
ideals of D, and {Iβ｜β∈B} be a
nonempty family of ideals of D with ∩β∈BIβ≠(0). Consider the following conditions:
(i) If P ⊆∪α∈APα then P = Pα for some α∈A;
(ii) If ∩β∈BIβ⊆P, then Iβ⊆P for some β ∈B.
In this paper, we prove that D satisfies (i)⇔D is a generalized weakly factorial domain of
dim(D)=1⇔D satisfies (ii)⇔D is a weakly Krull domain of dim(D)=1. We also study the
t-operation analogs of (i) and (ii).
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참고문헌 (12)
참고문헌 신청
B.G. Kang / 1989 / PrAufer v-multiplication domains and the ring R[X]Nv / J. Algebra 123 : 151 ~ 170
C.J. Hwang / 1999 / A note on coverings of prime ideals / Comm. Korean Math. Soc. 14 : 681 ~ 685
C.J. Hwang / 2005 / A covering condition for the prime spectrums / East Asian Math. J 21 : 61 ~ 64
C.M. Reis / 1970 / A compactness property for prime ideals in Noetherian rings / Proc. Amer. Math. Soc. 25 : 353 ~ 356
D.D. Anderson / 1992 / Finite character representation for integral domains / Bollettino U. M. I. 7 (6) : 613 ~ 630
C.J. Hwang / 1999 / A note on coverings of prime ideals / Comm. Korean Math. Soc. 14 : 681 ~ 685
C.J. Hwang / 2005 / A covering condition for the prime spectrums / East Asian Math. J 21 : 61 ~ 64
C.M. Reis / 1970 / A compactness property for prime ideals in Noetherian rings / Proc. Amer. Math. Soc. 25 : 353 ~ 356
D.D. Anderson / 1992 / Finite character representation for integral domains / Bollettino U. M. I. 7 (6) : 613 ~ 630
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