Non-absolutely irreducible elements in the ring of integer-valued polynomials

被引：7

作者：

Nakato, Sarah ^{[1
]}

机构：

[1] Graz Univ Technol, Inst Anal & Zahlentheorie, Kopernikusgasse 24, A-8010 Graz, Austria

来源：

COMMUNICATIONS IN ALGEBRA | 2020年 / 48卷 / 04期

基金：

奥地利科学基金会;

关键词：

Irreducible elements; absolutely irreducible elements; non-absolutely irreducible elements; integer-valued polynomials; FACTORIZATION; ELASTICITY;

D O I：

10.1080/00927872.2019.1705474

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a commutative ring with identity. An element is said to be absolutely irreducible in R if for all natural numbers n > 1, r(n) has essentially only one factorization namely If is irreducible in R but for some n > 1, r(n) has other factorizations distinct from then r is called non-absolutely irreducible. In this paper, we construct non-absolutely irreducible elements in the ring of integer-valued polynomials. We also give generalizations of these constructions.

引用

页码：1789 / 1802

页数：14

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