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math.AC2017
A realization theorem for sets of lengths in numerical monoids
Alfred Geroldinger, Wolfgang Schmid
We show that for every finite nonempty set L of integers greater than or equal to 2 there are a numerical monoid H and a squarefree element a H whose set of lengths L(a) is e…
math.AC2017
The monotone catenary degree of monoids of ideals
Alfred Geroldinger, Andreas Reinhart
Factoring ideals in integral domains is a central topic in multiplicative ideal theory. In the present paper we study monoids of ideals and consider factorizations of ideals into m…
math.AC2017★ 17 cited
Long sets of lengths with maximal elasticity
Alfred Geroldinger, Qinghai Zhong
We introduce a new invariant describing the structure of sets of lengths in atomic monoids and domains. For an atomic monoid , let be the set of all positive integers…