Elasticity in Apéry Sets

Abstract

A numerical semigroup S is an additive subsemigroup of the nonnegative integers, containing zero, with finite complement. Its multiplicity m is its smallest nonzero element. The Apéry set of S is the set of elements Ap(S) = {n ∈ S : n − m ∈ S}. Fixing a numerical semigroup, we ask how many elements of its Apéry set have nonunique factorization and define several new invariants.

Elasticities of Orders in Central Simple Algebras

“…Whereas the interest has initially been focused on commutative settings, in particular, on Krull domains, Krull monoids, and Mori monoids, the past decade has seen an increasing interest in studying the factorizations in noncommutative rings and monoids. While elasticities are some of the most basic invariants, they remain to be of central interest [Aut+20;Got20;GO20].…”