Research ArticleNo Access

Archimedean classes in additive monoids

Zur Izhakian

Department of Mathematics, Ariel University, 40700 Ariel, Israel

E-mail Address: zzur@g.ariel.ac.il

Corresponding author.

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and

Manfred Knebusch

Department of Mathematics, Universität Regensburg, 93040 Regensburg, Germany

E-mail Address: manfred.knebusch@mathematik.uni-regensburg.de

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https://doi.org/10.1142/S0219498825500148Cited by:0 (Source: Crossref)

Abstract

Summand absorbing submodules are common in modules over (additively) idempotent semirings, for example, in tropical algebra. A submodule $W$ $W$ of $V$ $V$ is summand absorbing, if $x + y \in W$ $x + y \in W$ implies $x \in W, y \in W$ $x \in W, y \in W$ for any $x, y \in V$ $x, y \in V$ . This paper proceeds the study of these submodules, and more generally of additive monoids, with emphasis on their archimedean classes and quotient structures.

Communicated by S. R. López-Permouth

Keywords:

AMSC: 14T05, 16D70, 16Y60, 06F05, 06F25, 13C10, 14N05

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