2025/09/18 by Jean‐Luc Marichal, Marichal, Jean-Luc, Pierre Mathonet +3
Computer Science · Decision Sciences · Mathematics · #16B99 #20M99 #20N15 #Commutative Algebra and Its Applications #FOS: Mathematics #Fuzzy and Soft Set Theory #Group Theory (math.GR) #Rings and Algebras (math.RA) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2509.14947
openalex publication_date 2025/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It was claimed in [4] that for any integer n\geqslant 2, a neutral element can be adjoined to an n-ary semigroup if and only if the n-ary semigroup is reducible to a binary semigroup. We show that the `only if' direction of this statement is incorrect when n is odd. Moreover, we offer a comprehensive characterization of the class of irreducible n-ary semigroups, for odd n, that admit the adjunction of a neutral element.