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Hu’s primal algebra theorem revisited. (English) Zbl 1048.08003

Summary: It is shown how Lawvere’s one-to-one translation between Birkhoff’s description of varieties and the categorical one [see F. W. Lawvere, Proc. Natl. Acad. Sci. USA 50, 869–872 (1963; Zbl 0119.25901)] turns Hu’s theorem on varieties generated by a primal algebra [see T. K. Hu, Math Z. 110, 180–198 (1969; Zbl 0175.28903), Algebra Univers. 1, 152–154 (1971; Zbl 0236.08005)] into a simple reformulation of the classical representation theorem of finite Boolean algebras as powerset algebras.

MSC:

08A40 Operations and polynomials in algebraic structures, primal algebras
08B99 Varieties
18C05 Equational categories
06D25 Post algebras (lattice-theoretic aspects)
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