Two Extensions of a Star Operation on D to the Polynomial Ring D[X]

IF 0.6 Q3 MATHEMATICS Kyungpook Mathematical Journal Pub Date : 2021-01-01 DOI:10.5666/KMJ.2021.61.1.23

G. Chang, Hwankoo Kim

引用次数: 0

Abstract

Let D be an integral domain with quotient field K, X an indeterminate over D, ∗ a star operation on D, and Cl∗(D) be the ∗-class group of D. The ∗w-operation on D is a star operation defined by I∗w = {x ∈ K | xJ ⊆ I for a nonzero finitely generated ideal J of D with J∗ = D}. In this paper, we study two star operations {∗} and [∗] on D[X] defined by A{∗} = ⋂ P∈∗w-Max(D) ADP [X] and A [∗] = ( ⋂ P∈∗w-Max(D) AD[X]P [X]) ∩ AK[X]. Among other things, we show that Cl∗(D) ∼= Cl[∗](D[X]) if and only if D is integrally

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D上的一个星型运算在多项式环D[X]上的两个扩展

设D是一个有商域K的积分域，X是D上的一个不定数，D上的一个* *运算，Cl * (D)是D上的* -类群。对于D的非零有限生成理想J，当J∗= D}时，D上的* w运算是一个由I∗w = {X∈K | xJ≠I定义的*运算。本文研究了D[X]上由A{∗}= P∈∗w-Max(D) ADP [X]和A[∗]= (P∈∗w-Max(D) AD[X]P [X])∩AK[X]定义的两个星形运算{∗}和[∗]。除其他事项外，我们证明当且仅当D是积分时，Cl∗(D) ~ = Cl[∗](D[X])

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来源期刊

Kyungpook Mathematical Journal MATHEMATICS-

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Kyungpook Mathematical Journal is an international journal devoted to significant research concerning all aspects of mathematics. The journal has a preference for papers having a broad interest. One volume of the journal is published every year. Each volume until volume 42 consisted of two issues; however, starting from volume 43(2003), each volume consists of four issues. Authors should strive for expository clarity and good literary style. Manuscripts should be prepared as follows. The first page must consist of a short descriptive title, followed by the name(s) and address(es) of the author(s) along with an electronic address if available.