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It is well-known that quasi-Pr\"{u}fer domains are characterized as those domains $D$, such that every extension of $D$ inside its quotient field is a primitive extension and that primitive extensions are characterized in terms of INC-extensions. Let $R=\bigoplus_{\alpha\in\Gamma}R_{\alpha}$ be a graded integral domain graded by an arbitrary torsionless grading monoid $\Gamma$ and $\star$ be a semistar operation on $R$. The main purpose of this paper is to give new characterizations of gr-$\star$-quasi-Pr\"{u}fer domains in terms of graded primitive and INC-extensions. Applications include new characterizations of UM$t$-domains.
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참고문헌 (19)
참고문헌 신청
D. D. Anderson / 1982 / Divisibility properties of graded domains / Canad. J. Math. 34(1):196~215
D. F. Anderson / 2013 / Graded integral domains and Nagata rings / J. Algebra 387:169~184
A. Ayache / 1997 / Residually algebraic pairs of rings / Math. Z. 225(1):49~65
G. W. Chang / 2009 / Uppers to zero in polynomial rings and Prufer-like domains / Comm. Algebra 37(1):164~192
G. W. Chang / Discrete valuation overrings of a graded Noetherian domain / J. Commut.
D. F. Anderson / 2013 / Graded integral domains and Nagata rings / J. Algebra 387:169~184
A. Ayache / 1997 / Residually algebraic pairs of rings / Math. Z. 225(1):49~65
G. W. Chang / 2009 / Uppers to zero in polynomial rings and Prufer-like domains / Comm. Algebra 37(1):164~192
G. W. Chang / Discrete valuation overrings of a graded Noetherian domain / J. Commut.
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