대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제33권2호
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  • Pages.397-408
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  • 2018
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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GRADED PRIMITIVE AND INC-EXTENSIONS

  • Hamdi, Haleh (Department of Pure Mathematics Faculty of Mathematical Sciences University of Tabriz) ;
  • Sahandi, Parviz (Department of Pure Mathematics Faculty of Mathematical Sciences University of Tabriz)
  • 투고 : 2017.05.31
  • 심사 : 2017.09.04
  • 발행 : 2018.04.30
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초록

It is well-known that quasi-$Pr{\ddot{u}}fer$ 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-$Pr{\ddot{u}}fer$ domains in terms of graded primitive and INC-extensions. Applications include new characterizations of UMt-domains.

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참고문헌

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