The Lattice of Subvarieties of Semilattice Ordered Algebras
Agata Pilitowska, Anna Zamojska-Dzienio · Order · 2013
This paper is devoted to the semilattice ordered $\mathcal{V}$ -algebras of the form (A, Ω, + ), where + is a join-semilattice operation and (A, Ω) is an algebra from some given variety $\mathcal{V}$ . 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 ordered $\mathcal{V}$ -algebras in relation to the lattice of subvarieties of the variety $\mathcal{V}$ .