ON FACTORIZATION IN BLOCK MONOIDS FORMED BY ${ar{1},ar{a}}$ IN $mathbb{Z}_{n}$

[摘要] We consider the factorization properties of block monoids on $mathbb{Z}_n$ determined by subsets of the form $S_a={ar{1},ar{a}}$. We denote such a block monoid by $mathcal{B}_a(n)$. In §2, we provide a method based on the division algorithm for determining the irreducible elements of $mathcal{B}_a(n)$. Section 3 offers a method to determine the elasticity of $mathcal{B}_a(n)$ based solely on the cross number. Section 4 applies the results of §3 to investigate the complete set of elasticities of Krull monoids with divisor class group $mathbb{Z}_n$.AMS 2000 Mathematics subject classification: Primary 20M14; 20D60; 13F05

[学科分类] 数学（综合）

[关键词] block monoid;elasticity of factorization;Krull monoid