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elasticity of factorization

Proceedings of the Edinburgh Mathematical Society (1)

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ON FACTORIZATION IN BLOCK MONOIDS FORMED BY $\{\bar{1},\bar{a}\}$ IN $\mathbb{Z}_{n}$
Scott T. Chapman, William W. Smith
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 46 / Issue 2 / June 2003

Published online by Cambridge University Press:

04 July 2003, pp. 257-267
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We consider the factorization properties of block monoids on $\mathbb{Z}_n$ determined by subsets of the form $S_a=\{\bar{1},\bar{a}\}$. 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