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Complement-Finite Ideals

In: Algebraic, Number Theoretic, and Topological Aspects of Ring Theory

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  • N. Baeth

    (Franklin and Marshall College, Department of Mathematics)

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.

Suggested Citation

  • N. Baeth, 2023. "Complement-Finite Ideals," Springer Books, in: Jean-Luc Chabert & Marco Fontana & Sophie Frisch & Sarah Glaz & Keith Johnson (ed.), Algebraic, Number Theoretic, and Topological Aspects of Ring Theory, pages 61-86, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-28847-0_5
    DOI: 10.1007/978-3-031-28847-0_5
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