[en] It was claimed in [4] that for any integer n>=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.
Disciplines :
Mathematics
Author, co-author :
MARICHAL, Jean-Luc ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
MATHONET, Pierre; ULg - University of Liège > Mathematics
WALDHAUSER, Tamás; University of Szeged, Bolyai Institute
Language :
English
Title :
Irreducible polyadic semigroups admitting the adjunction of a neutral element
