TY - JOUR

T1 - The congruences on the semigroup of balanced transformations of an infinite set

AU - Marques-Smith, M.P.O.

AU - Sullivan, Robert

PY - 2000

Y1 - 2000

N2 - In 1966, J. M. Howie (J. London Math. Sec. 41, 707-716) showed that the semigroup generated by all non-identity idempotent transformations of an infinite set X is the disjoint union of two semigroups, one of which is denoted by H and consists of all balanced transformations of X (that is, all transformations whose defect, shift, and collapse are equal and infinite). Subsequently, J. M. Howie (1981, Proc. Roy Sec. Edinburgh Sect. A 88, 159-167, 169-184) and Marques (1983, Proc. Roy. Sec. Edinburgh Sect. A 93, 245-257) showed that certain Rees quotient semigroups associated with H are congruence-free. Here, we describe all congruences on H. (C) 2000 Academic Press.

AB - In 1966, J. M. Howie (J. London Math. Sec. 41, 707-716) showed that the semigroup generated by all non-identity idempotent transformations of an infinite set X is the disjoint union of two semigroups, one of which is denoted by H and consists of all balanced transformations of X (that is, all transformations whose defect, shift, and collapse are equal and infinite). Subsequently, J. M. Howie (1981, Proc. Roy Sec. Edinburgh Sect. A 88, 159-167, 169-184) and Marques (1983, Proc. Roy. Sec. Edinburgh Sect. A 93, 245-257) showed that certain Rees quotient semigroups associated with H are congruence-free. Here, we describe all congruences on H. (C) 2000 Academic Press.

U2 - 10.1006/jabr.2000.8391

DO - 10.1006/jabr.2000.8391

M3 - Article

VL - 234

SP - 1

EP - 30

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -