Bibliographic Information: Mudrinski, N., & Sobot, M. (2024). Commutators in Semirings. arXiv:2410.09271v1 [math.RA].
Research Objective: The paper aims to characterize abelian, nilpotent, and solvable semirings with absorbing zero by analyzing the behavior of commutators within these algebraic structures.
Methodology: The authors utilize concepts from universal algebra, specifically term condition commutators, to define and analyze nilpotency, solvability, and supernilpotency in semirings. They establish connections between these properties and the ideal structure of semirings.
Key Findings:
Main Conclusions: The properties of abelian, nilpotent, and solvable semirings with absorbing zero can be fully described by examining the additive cancellativity and the behavior of ideal products within these semirings.
Significance: This research contributes to the understanding of semirings, an algebraic structure with applications in various fields like computer science and optimization, by providing new insights into their properties related to commutators.
Limitations and Future Research: The paper primarily focuses on semirings with absorbing zero. Further research could explore similar characterizations for broader classes of semirings or investigate the implications of these findings in specific application domains.
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