Right-orderability versus left-orderability for monoids

Friedrich Wehrung (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We investigate the relationship between (total) left- and right-orderability for monoids, in particular illustrating the finite case by various structural observations and counterexamples, also highlighting the particular role played by \emph{positive} orderability. Moreover, we construct a non-left-orderable, positively right-orderable submonoid of the free product of the cyclic group of order 7 with the free group on four generators. Any group extension of that monoid has elements of order 7.

Mots clés: group; universal group; cancellative; conical; category; universal monoid; right order; Monoid

Domaines: Mathématiques générales [math.GM]

Friedrich Wehrung. Right-orderability versus left-orderability for monoids. Semigroup Forum, 2021, 102 (3), pp.885--899. ⟨10.1007/s00233-021-10185-y⟩. ⟨hal-02872310v2⟩