Abstract

An extension of integral domains $A\subseteq B$ is called a quasi-divisor closed extension if, whenever $b_1{b}_2\in A$ for some nonzero $b_1,b_2\in B,$ then there exist units u, v of B such that $b_{1}u,b_{2}v\in A.$ 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.

中文翻译：

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除数闭和拟除数闭扩展

摘要

积分域的扩展 $\mathrm{一种}\subseteq 乙$ 被称为拟除数封闭扩展，如果，无论何时 ${乙}_1{乙}_2\in \mathrm{一种}$ 对于一些非零 ${乙}_1,{乙}_2\in 乙,$则存在单位ü，v的乙使得${乙}_1你,{乙}_{2}v\in \mathrm{一种}.$拟除数闭扩展的概念是除数闭扩展的概念的推广。在本文中，我们证明了积分域的除数闭扩展和拟除数闭扩展的一些新结果。特别是，我们研究了分级域的准除数封闭扩展，其中分级超过分级幺半群。