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Result.Math. 49 (2006), 187200 c 2006 Birkhauser Verlag Basel/Switzerland

Summary: Result.Math. 49 (2006), 187­200
c 2006 Birkh¨auser Verlag Basel/Switzerland
1422-6383/040187-14, published online December 5, 2006
DOI 10.1007/s00025-006-0219-z Results in Mathematics
Elastic Properties and Prime Elements
Paul Baginski, Scott T. Chapman, Christopher Crutchfield,
K. Grace Kennedy and Matthew Wright
Abstract. In a commutative, cancellative, atomic monoid M, the elasticity of
a non-unit x is defined to be (x) = L(x)/l(x), where L(x) is the supremum of
the lengths of factorizations of x into irreducibles and l(x) is the corresponding
infimum. The elasticity (M) of M is given as the supremum of the elasticities
of the nonzero non-units in the domain. We call (M) accepted if there exists
a non-unit x M with (M) = (x). In this paper, we show for a monoid M
with accepted elasticity that
{(x) | x a non-unit of M} = Q [1, (M)]
if M has a prime element. We develop the ideas of taut and flexible elements
to study the set {(x) | x a non-unit of M} when M does not possess a prime
Mathematics Subject Classification (2000). 20M14, 13F20, 13F15.
Keywords. Elasticity of factorization, prime element, numerical monoid.


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics