Freese, R.; Ježek, J.; Jipsen, P.; Marković, P.; Maróti, M.; McKenzie, R. The variety generated by order algebras. (English) Zbl 1058.08001 Algebra Univers. 47, No. 2, 103-138 (2002). Every ordered set \((A,\leq )\) can be considered as an algebra \((A,\cdot )\) in a natural way, where \(xy=x\) iff \(x\leq y\) and \(xy=y\) otherwise. The variety generated by order algebras is investigated. It is proved, among other things, that this variety is not finitely based and, although locally finite, it is not contained in any finitely generated variety. Also, the bottom of the lattice of its subvarieties is described. Reviewer: Radomír Halaš (Olomouc) Cited in 5 Documents MSC: 08A05 Structure theory of algebraic structures 08B15 Lattices of varieties 06A11 Algebraic aspects of posets Keywords:ordered set; variety generated by order algebras; lattice of subvarieties PDFBibTeX XMLCite \textit{R. Freese} et al., Algebra Univers. 47, No. 2, 103--138 (2002; Zbl 1058.08001) Full Text: DOI Link