Accepted Elasticity in Local Arithmetic Congruence Monoids

  title={Accepted Elasticity in Local Arithmetic Congruence Monoids},
  author={Lorin Crawford and Vadim Ponomarenko and Jason Steinberg and Mark Williams},
For certain a, b ∈ N, the Arithmetic Congruence Monoid M(a, b) is a multiplicatively closed subset of N given by {x ∈ N : x ≡ a (mod b)}∪{1}. An irreducible in this monoid is any element that cannot be factored into two elements, each greater than 1. Each monoid element (apart from 1) may be factored into irreducibles in at least one way. The elasticity of a monoid element (apart from 1) is the length of the longest factorization into irreducibles, divided by the length of the shortest… CONTINUE READING