How Do You Measure Primality?

被引：9

作者：

O'Neill, Christopher ^{[1
]}

Pelayo, Roberto ^{[2
]}

机构：

[1] Texas A&M Univ, College Stn, TX 77840 USA

[2] Univ Hawaii, Hilo, HI 96720 USA

来源：

AMERICAN MATHEMATICAL MONTHLY | 2015年 / 122卷 / 02期

基金：

美国国家科学基金会;

关键词：

NUMERICAL MONOIDS; BLOCK MONOIDS; TAME DEGREE; ELASTICITY; CATENARY;

D O I：

10.4169/amer.math.monthly.122.02.121

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In commutative monoids, the omega-value measures how far an element is from being prime. This invariant, which is important in understanding the factorization theory of monoids, has been the focus of much recent study. This paper provides detailed examples and an overview of known results on omega-primality, including several recent and surprising contributions in the setting of numerical monoids. As many questions related to w-primality remain, we provide a list of open problems accessible to advanced undergraduate students and beginning graduate students.

引用

页码：121 / 137

页数：17

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