2024/04/11 by David Dolžan, Dolžan, David
Computer Science · Decision Sciences · #Advanced Algebra and Logic #Constraint Satisfaction and Optimization #FOS: Mathematics #Fuzzy and Soft Set Theory #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2404.07623
openalex publication_date 2024/04/11 · openalex created_date 2024/04/13 · openalex updated_date 2026/07/28
We prove that a semiring multiplicatively generated by its idempotents is commutative and Boolean, if every idempotent in the semiring has an orthogonal complement. We prove that a semiring additively generated by its idempotents is commutative, if every idempotent in the semiring has an orthogonal complement and all the nilpotents in the semirings are central. We also provide examples that the assumptions on the existence of orthogonal complements of idempotents and the centrality of nilpotents cannot be omitted.