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Let $D$ be an integral domain, $X$ be an indeterminate over $D$, $D[X]$ be the polynomial ring over $D$, and $D(X)$ be the Nagata ring of $D$. Let $[d]$ be the star operation on $D[X]$, which is an extension of the $d$-operation on $D$ as in [5, Theorem 2.3]. In this paper, we show that $D$ is a sharp domain if and only if $D[X]$ is a $[d]$-sharp domain, if and only if $D(X)$ is a sharp domain.
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참고문헌 (11)
참고문헌 신청
Z. Ahmad / 2012 / A Schreier domain type condition / Bull. Math. Soc. Sci. Math. Roumanie 55:241~247
Z. Ahmad / 2015 / A Schreier Domain Type Condition II / Algebra Colloquium 22:923~934
D.D. Anderson / 2000 / Two star-operations and their induced lattices / Comm. Algebra 28:2461~2475
G.W. Chang / 2005 / Strong Mori domains and the ring D[X]Nv / J. Pure Appl. Algebra 197:293~304
G.W. Chang / 2007 / Uppers to zero and semistar operations in poly-nomial rings / J. Algebra 318:484~493
Z. Ahmad / 2015 / A Schreier Domain Type Condition II / Algebra Colloquium 22:923~934
D.D. Anderson / 2000 / Two star-operations and their induced lattices / Comm. Algebra 28:2461~2475
G.W. Chang / 2005 / Strong Mori domains and the ring D[X]Nv / J. Pure Appl. Algebra 197:293~304
G.W. Chang / 2007 / Uppers to zero and semistar operations in poly-nomial rings / J. Algebra 318:484~493
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