caa a22 4500 445344938 CHVBK 20180317142826.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00233-010-9280-8 doi (NATIONALLICENCE)springer-10.1007/s00233-010-9280-8 An elegant 3-basis for inverse semigroups [Elektronische Daten] [João Araújo, Michael Kinyon] It is well known that in every inverse semigroup the binary operation and the unary operation of inversion satisfy the following three identities: $$x=(xx')x, \qquad(xx')(y'y)=(y'y)(xx'), \qquad(xy)z=x(yz'') .$$ The goal of this note is to prove the converse, that is, we prove that an algebra of type 〈2,1〉 satisfying these three identities is an inverse semigroup and the unary operation coincides with the usual inversion on such semigroups. Springer Science+Business Media, LLC, 2010 Inverse semigroups nationallicence Equational logic nationallicence Araújo João Centro de Álgebra, Universidade de Lisboa, 1649-003, Lisboa, Portugal aut Kinyon Michael Department of Mathematics, University of Denver, 2360 S Gaylord St, 80208, Denver, CO, USA aut Semigroup Forum Springer-Verlag 82/2(2011-04-01), 319-323 0037-1912 82:2<319 2011 82 233 https://doi.org/10.1007/s00233-010-9280-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00233-010-9280-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Araújo João Centro de Álgebra, Universidade de Lisboa, 1649-003, Lisboa, Portugal aut NATIONALLICENCE 700 1- Kinyon Michael Department of Mathematics, University of Denver, 2360 S Gaylord St, 80208, Denver, CO, USA aut NATIONALLICENCE 773 0- Semigroup Forum Springer-Verlag 82/2(2011-04-01), 319-323 0037-1912 82:2<319 2011 82 233 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer