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Divisor closed and quasi-divisor closed extensions

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Abstract An extension of integral domains is called a quasi-divisor closed extension if, whenever for some nonzero then there exist units u, v of B such that The notion of… Click to show full abstract

Abstract An extension of integral domains is called a quasi-divisor closed extension if, whenever for some nonzero then there exist units u, v of B such that The notion of a quasi-divisor closed extension is a generalization of that of a divisor closed extension. In this article, we prove some new results about divisor closed extensions and quasi-divisor closed extensions of integral domains. In particular, we study quasi-divisor closed extensions of graded domains, where the grading is over grading monoids.

Keywords: quasi divisor; divisor; divisor closed; extension; closed extensions

Journal Title: Communications in Algebra
Year Published: 2021

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