On transitive linear semigroups

This paper deals with semigroups of linear transformations which act transi tively on a finite-dimensional vector space. An explicit canonical form is obtained for the semigroups which lack proper transitive left ideals. The c lass of such semigroups can be considered to be an extention of the class o f transitive groups. It contains all minimal transitive (and hence all shar ply transitive) semigroups. (C) 2000 Elsevier Science Inc. All rights reser ved.