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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2021.1
- 수록면
- 23 - 32 (10page)
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Let D be an integral domain with quotient field K, X an indeterminate over D, ? a star operation on D, and Cl?(D) be the ?-class group of D. The ?w-operation on D is a star operation defined by I?w = {x ∈ K | xJ ⊆ I for a nonzero finitely generated ideal J of D with J? = D}. In this paper, we study two star operations {?} and [?] on D[X] defined by A{?} = ∩P ∈?w-Max(D) ADP [X] and A[?] = ( ∩P ∈?w-Max(D) AD[X]P [X]) ∩ AK[X]. Among other things, we show that Cl?(D) ∼= Cl[?] (D[X]) if and only if D is integrally closed.
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참고문헌 (13)
참고문헌 신청
D. D. Anderson / 2000 / Two star operations and their induced lattices / Comm. Algebra 28:2461~2475
J. W. Brewer / 1979 / Seminormality and projective modules over polynomial rings / J. Algebra 58:208~216
G. W. Chang / 2006 / ∗-Noetherian domains and the ring D[X]N∗ / J. Algebra 297:216~233
G. W. Chang / 2007 / Upper to zero and semistar operations in polynomial rings / J. Algebra 318:484~493
G. W. Chang / 2011 / An overring-theoretic approach to polynomial extensions of star and semistar operations / Comm. Algebra 39:1956~1978
J. W. Brewer / 1979 / Seminormality and projective modules over polynomial rings / J. Algebra 58:208~216
G. W. Chang / 2006 / ∗-Noetherian domains and the ring D[X]N∗ / J. Algebra 297:216~233
G. W. Chang / 2007 / Upper to zero and semistar operations in polynomial rings / J. Algebra 318:484~493
G. W. Chang / 2011 / An overring-theoretic approach to polynomial extensions of star and semistar operations / Comm. Algebra 39:1956~1978
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