Complement-Finite Ideals

N. Baeth ()
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N. Baeth: Franklin and Marshall College, Department of Mathematics

A chapter in Algebraic, Number Theoretic, and Topological Aspects of Ring Theory, 2023, pp 61-86 from Springer

Abstract: Abstract We introduce a new class of commutative cancellative monoids which we call complement-finite ideals. Submonoids of free abelian monoids, these abstract monoids generalize the multiplicative structure of numerical monoids and are also closely related to monoids of zero-sum sequences and certain affine monoids. Here we provide a first general study of this more general construction. Specifically, we study the algebraic and arithmetic properties of complement-finite ideals and provide examples to illustrate their connections to other objects readily found in the literature.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-28847-0_5

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DOI: 10.1007/978-3-031-28847-0_5

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