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This paper is devoted to the semilattice ordered -algebras of the form (A, Ω, + ), where + is a join-semilattice operation and (A, Ω) is an algebra from some given variety . We characterize the free semilattice ordered algebras using the concept of extended power algebras. Next we apply the result to describe the lattice of subvarieties of the variety of semilattice...
Denote by Sn the variety generated by all semigroups of order n. Marcel Jackson proved that the variety Sn contains uncountably many subvarieties if n⩾4, and it follows from existing results that the variety S2 contains precisely 32 subvarieties. However, the number of subvarieties of the variety S3 has been unknown. The main aim of the present article is to address this problem. It is shown that...
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