Amalgamation and extensions of summand absorbing modules over a semiring

Zur Izhakian; Manfred Knebusch

doi:10.1142/S0219498822501249

Amalgamation and extensions of summand absorbing modules over a semiring

Zur Izhakian^* (Corresponding Author), Manfred Knebusch

^*Corresponding author for this work

Mathematical Science

University of Regensburg

Research output: Contribution to journal › Article › peer-review

Abstract

A submodule W of V is summand absorbing, if x+y∈W implies x∈W,y∈W for any x,y∈V. Such submodules often appear in modules over (additively) idempotent semirings, particularly in tropical algebra. This paper studies amalgamation and extensions of these submodules, and more generally of upper bound modules.

Original language	English
Article number	2250124
Number of pages	33
Journal	Journal of Algebra and its Applications
Volume	21
Issue number	6
Early online date	18 Mar 2021
DOIs	https://doi.org/10.1142/S0219498822501249
Publication status	Published - Jun 2022

Keywords

math.RA
semiring
lacking zero sums
Direct sum decomposition
free (semi)module
projective (semi)module
Indecomposable
semidirect complement
amalgamation
extension

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10.1142/S0219498822501249

https://arxiv.org/abs/2007.06215Licence: Unspecified

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KW - semiring

KW - lacking zero sums

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KW - semidirect complement

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Amalgamation and extensions of summand absorbing modules over a semiring

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Keywords

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