The Lattice of Subvarieties of Semilattice Ordered Algebras

• DOI: 10.1007/s11083-013-9297-1
• Publication Date: 2013-06-19T01:58:35Z
• Authors: A. Pilitowska; A. Zamojska-Dzienio
• Keywords: Algebra and Number Theory; Computational Theory and Mathematics; Geometry and Topology; 0102 computer and information sciences; 01 natural sciences

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 \(\mathcal{V}\).