JP Journal of Algebra, Number Theory and Applications
Volume 44, Issue 1, Pages 63 - 80
(October 2019) http://dx.doi.org/10.17654/NT044010063 |
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THE NUMBER OF ADDENDS IN THE DECOMPOSITION OF AN ELEMENT OF A NUMERICAL MONOID INTO ATOMS
Hamid Kulosman
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Abstract: It was proved in 2018 by Geroldinger and Schmid [3] that for every nonempty subset Σ of there exist a numerical monoid T and an element x of T such that a natural number n is the number of atoms in a decomposition of x into a sum of atoms if and only if n belongs to Σ. We give a completely different proof for The different approach that we offer can shed some additional light on this and related problems, some of which are open. |
Keywords and phrases: numerical monoid, atoms, irreducible elements, factorization process, addendization.
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