Abstract. It is known that varieties of semilattice-ordered semigroups are in one-to-one correspondence with the ordered pairs $(\rho,[ ])$ where $\rho $ is a fully invariant congruence on the free semigroup on a countably infinite set and $[ ]$ is a $\rho $-admissible closure operator. We find all admissible closure operators for varieties of left normal bands. Using the obtained results we describe all varieties of semilattice-ordered left normal bands by admissible closure operators. We solve the identity problem for all varieties of semilattice-ordered normal bands.

DOI: 10.14232/actasm-016-777-4

AMS Subject Classification (1991): 06F05, 08B15, 20M07

Keyword(s): variety, semilattice-ordered semigroup, normal band, admissible closure operator

Received April 29, 2016, and in revised form October 20, 2016. (Registered under 27/2016.)