Classes of semigroups modulo Green's relation H

Xavier Mary (1, 2)

1 MODAL'X - Modélisation aléatoire de Paris X
2 FP2M - Fédération Parisienne de Modélisation Mathématique

THIS IS THE PREPRINT VERSION OF THE ARTICLE. Inverses semigroups and orthodox semigroups are either defined in terms of inverses, or in terms of the set of idempotents E(S). In this article, we study analogs of these semigroups defined in terms of inverses modulo Green's relation H, or in terms of the set of group invertible elements H(S), that allows a study of non-regular semigroups. We then study the interplays between these new classes of semigroups, as well as with known classes of semigroups (notably inverse, orthodox and cryptic semigroups)

Mots clés: semigroups; Green's relations; generalized inverses

Domaines: Théorie des groupes [math.GR]

Xavier Mary. Classes of semigroups modulo Green's relation H. Semigroup Forum, 2014, 88 (3), pp.647-669. ⟨10.1007/s00233-013-9557-9⟩. ⟨hal-00679837⟩