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Divisor closed and quasi-divisor closed extensions
Communications in Algebra ( IF 0.6 ) Pub Date : 2021-03-12 , DOI: 10.1080/00927872.2021.1898629
Dibyendu Mondal 1
Affiliation  

Abstract

An extension of integral domains AB is called a quasi-divisor closed extension if, whenever b1b2A for some nonzero b1,b2B, then there exist units u, v of B such that b1u,b2vA. 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:

除数闭和拟除数闭扩展

摘要

积分域的扩展 一种 被称为拟除数封闭扩展,如果,无论何时 12一种 对于一些非零 1,2,则存在单位üv使得1,2v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。

更新日期:2021-03-12
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