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.)
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