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DOI 10.1007/s00025-006-0219-z Results in Mathematics Elastic Properties and Prime Elements

By Paul Baginski, Scott T. Chapman, Christopher Crutchfield, K. Grace Kennedy and Matthew Wright

Abstract

Abstract. In a commutative, cancellative, atomic monoid M, the elasticity of a non-unit x is defined to be ρ(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 ρ(M) ofM is given as the supremum of the elasticities of the nonzero non-units in the domain. We call ρ(M) accepted if there exists a non-unit x ∈ M with ρ(M) =ρ(x). In this paper, we show for a monoid M with accepted elasticity that {ρ(x) | x a non-unit of M} = Q ∩ [1,ρ(M)] if M has a prime element. We develop the ideas of taut and flexible elements to study the set {ρ(x) | x a non-unit of M} when M does not possess a prime element

Topics: prime element, numerical monoid
Year: 1422
OAI identifier: oai:CiteSeerX.psu:10.1.1.370.738
Provided by: CiteSeerX
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