Abstract
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 \(\mathcal{V}\).
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While working on this paper, the authors were supported by the Statutory Grant of Warsaw University of Technology 504P/1120/0025/000.
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Pilitowska, A., Zamojska-Dzienio, A. The Lattice of Subvarieties of Semilattice Ordered Algebras. Order 31, 217–238 (2014). https://doi.org/10.1007/s11083-013-9297-1
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DOI: https://doi.org/10.1007/s11083-013-9297-1
Keywords
- Ordered structures
- Semilattices
- Power algebras
- Free algebras
- Fully invariant congruences
- Varieties
- Lattice of subvarieties