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Almost subtractive submonoids of additive monoids and related quadratic forms

  • Zur Izhakian
  • Manfred Knebusch
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Abstract

We introduce and study the class of almost subtractive submonoids of additive monoids. This property relaxes the strict condition of subtractivity while still allowing for a simulated subtraction operation sufficient for many algebraic applications. We explore the structural properties of these monoids and demonstrate their significance in the theory of modules over semirings, specifically regarding quadratic forms and their companions.

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Cite

BibTeXRIS
BibTeX
@misc{izhakian2026almost,
  title = {{Almost subtractive submonoids of additive monoids and related quadratic forms}},
  author = {Zur Izhakian and Manfred Knebusch},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28356},
  eprint = {2609.28356},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28356},
}
RIS
TY  - UNPB
TI  - Almost subtractive submonoids of additive monoids and related quadratic forms
AU  - Zur Izhakian
AU  - Manfred Knebusch
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28356
UR  - https://arxiv.org/abs/2609.28356
AB  - We introduce and study the class of almost subtractive submonoids of additive monoids. This property relaxes the strict condition of subtractivity while still allowing for a simulated subtraction operation sufficient for many algebraic applications. We explore the structural properties of these monoids and demonstrate their significance in the theory of modules over semirings, specifically regarding quadratic forms and their companions.
ER  -