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http://dx.doi.org/10.4134/CKMS.c170230

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)
Publication Information
Communications of the Korean Mathematical Society / v.33, no.2, 2018 , pp. 397-408 More about this Journal
Abstract
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.
Keywords
semistar operation; graded domain; UMt-domain; primitive extension; INC-extension;
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Times Cited By KSCI : 2  (Citation Analysis)
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