The catenary degrees of elements in numerical monoids generated by arithmetic sequences

被引：6

作者：

Chapman, Scott T. ^{[1
]}

Corrales, Marly ^{[2
]}

Miller, Andrew ^{[3
]}

Miller, Chris ^{[4
]}

Patel, Dhir ^{[5
]}

机构：

[1] Sam Houston State Univ, Dept Math, Box 2206, Huntsville, TX 77341 USA

[2] Univ Southern Calif, Dept Math, Los Angeles, CA USA

[3] Amherst Coll, Dept Math, Amherst, MA 01002 USA

[4] Univ Wisconsin Madison, Dept Math, Madison, WI USA

[5] Rutgers State Univ, Dept Math, Hill Ctr Math Sci, Piscataway, NJ USA

来源：

COMMUNICATIONS IN ALGEBRA | 2017年 / 45卷 / 12期

基金：

美国国家科学基金会;

关键词：

Catenary degree; non-unique factorizations; numerical monoid; 20M13; 20M14; 11D05; TAME DEGREE; KRULL MONOIDS; DOMAINS;

D O I：

10.1080/00927872.2017.1310878

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We compute the catenary degree of elements contained in numerical monoids generated by arithmetic sequences. We find that this can be done by describing each element in terms of the cardinality of its length set and of its set of factorizations. As a corollary, we find for such monoids that the catenary degree becomes fixed on large elements. This allows us to define and compute the dissonance number- the largest element with a catenary degree different from the fixed value. We determine the dissonance number in terms of the arithmetic sequence's starting point and its number of generators.

引用

页码：5443 / 5452

页数：10

共 45 条

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