In: Mathematica Slovaca, vol. 57, no. 5
Gerard J. Chang - Scott T. Chapman - William W. Smith
Detaily:
Rok, strany: 2007, 415 - 454
O článku:
This paper continues the study begun in [\uppercase{Geroldinger}, A.: \textit{On non-unique factorizations into irreducible elements II}, Colloq. Math. Soc. János Bolyai \textbf{51} (1987), 723–757] concerning factorization properties of block monoids of the form $\mathcal{B}(\Zn, S)$ where $S=\{\overline{1}, \overline{a}\}$ (hereafter denoted $\mathcal{B}a(n)$). We introduce in Section 2 the notion of a \textit{Euclidean table} and show in Theorem 2.8 how it can be used to identify the irreducible elements of $\mathcal{B}a(n)$. In Section 3 we use the Euclidean table to compute the elasticity of $\mathcal{B}a(n)$ (Theorem 3.4). Section 4 considers the problem, for a fixed value of $n$, of computing the complete set of elasticities of the $\mathcal{B}a(n)$ monoids. When $n=p$ is a prime integer, Proposition 4.12 computes the three smallest possible elasticities of the $\mathcal{B}a(p)$.
Ako citovať:
ISO 690:
Chang, G., Chapman, S., Smith, W. 2007. Elasticity in certain block monoids via the Euclidean table. In Mathematica Slovaca, vol. 57, no.5, pp. 415-454. 0139-9918.
APA:
Chang, G., Chapman, S., Smith, W. (2007). Elasticity in certain block monoids via the Euclidean table. Mathematica Slovaca, 57(5), 415-454. 0139-9918.