caa a22 4500 388091746 CHVBK 20180307125253.0 cr unu---uuuuu 161130e199910 xx s 000 0 eng 10.1017/S0004972700036418 doi S0004972700036418 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700036418 The ideal structure of nilpotent-generated transformation semigroups [Elektronische Daten] In 1987 Sullivan determined the elements of the semigroup N(X) generated by all nilpotent partial transformations of an infinite set X; and later in 1997 he studied subsemigroups of N(X) defined by restricting the index of the nilpotents and the cardinality of the set. Here, we describe the ideals and Green's relations on such semigroups, like Reynolds and Sullivan did in 1985 for the semigroup generated by all idempotent total transformations of X. We then use this information to describe the congruences on certain Rees factor semigroups and to construct families of congruence-free semigroups with interesting algebraic properties. We also study analogous questions for X finite and for one-to-one partial transformations. Copyright © Australian Mathematical Society 1999 Marques-Smith M. Paula O. Centro de Matematica, Universidade do Minho, 4700 Braga, Portugal Sullivan R.P. Department of Mathematics and Statistics, Sultanb Qaboos University, Oman and Department of Mathematics, University of Western Australia, Nedlands WA 6907, Australia Bulletin of the Australian Mathematical Society Cambridge University Press 60/2(1999-10), 303-318 0004-9727 60:2<303 1999 60 BAZ https://doi.org/10.1017/S0004972700036418 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700036418 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Marques-Smith M. Paula O. Centro de Matematica, Universidade do Minho, 4700 Braga, Portugal NATIONALLICENCE 700 1- Sullivan R.P. Department of Mathematics and Statistics, Sultanb Qaboos University, Oman and Department of Mathematics, University of Western Australia, Nedlands WA 6907, Australia NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 60/2(1999-10), 303-318 0004-9727 60:2<303 1999 60 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge