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Cancellation among finite unary algebras. (English) Zbl 0859.08003
L. Lovász showed [Acta Math. Acad. Sci. Hung. 18, 321-328 (1967; Zbl 0174.01401)] that every finite algebra having a one-element subalgebra is cancellable among finite algebras. The present authors prove the converse for finite unary algebras.
Reviewer: M.Armbrust (Köln)

##### MSC:
 08A60 Unary algebras 08A05 Structure theory of algebraic structures
##### Keywords:
direct product; cancellation; finite unary algebras
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##### References:
 [1] Appleson, R.R.; Lovász, L., A characterization of cancellable k-ary structures, Period. math. hungar., 6, 17-19, (1975) · Zbl 0306.08001 [2] Lovász, L., Operations with structures, Acta math. acad. sci. hungar., 18, 321-328, (1967) · Zbl 0174.01401 [3] Lovász, L., On the cancellation law among finite relational structures, Period. math. hungar., 1, 145-156, (1971) · Zbl 0223.08002 [4] McKenzie, R.; McNulty, G.; Taylor, W., ()
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