On the Number of Factorizations of an Element in an Atomic Monoid
نویسندگان
چکیده
Let S be a reduced commutative cancellative atomic monoid. If s is a nonzero element of S, then we explore problems related to the computation of η(s), which represents the number of distinct irreducible factorizations of s ∈ S. In particular, if S is a saturated submonoid of Nd , then we provide an algorithm for computing the positive integer r(s) for which 0 < lim n→∞ η(sn) nr(s)−1 <∞. We further show that r(s) is constant on the Archimedean components of S. We apply the algorithm to show how to compute lim n→∞ η(sn) nr(s)−1 and also consider various stability conditions studied earlier for Krull monoids with finite divisor class group. 2002 Elsevier Science (USA). All rights reserved. ✩ This paper has been supported by the projects DGES PB96-1424 and BFM 2000-1469. * Corresponding author. E-mail addresses: [email protected] (S.T. Chapman), [email protected] (J.I. García-García), [email protected] (P.A. García-Sánchez), [email protected] (J.C. Rosales). 1 This work was started while the author was on an Academic Leave granted by the Faculty Development Committee at Trinity University. He also wishes to thank the Departmento de Álgebra, Universidad de Granada for their support and hospitality. 0196-8858/02/$ – see front matter 2002 Elsevier Science (USA). All rights reserved. PII: S0196-8858(02) 00 02 58 S.T. Chapman et al. / Advances in Applied Mathematics 29 (2002) 438–453 439
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