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Monounary algebras and bottleneck algebras. (English) Zbl 0935.08003
A bottleneck algebra is a triple \((R, \max , \min)\), where \(R\) is a linearly ordered set. A monounary algebra \((M,f)\) is b-representable if there exists a bottleneck algebra \(R\), a positive integer \(n\) and a matrix \(A\) of type \(n\times n\) with elements from \(R\) such that \((M,f)\) is isomorphic to a subalgebra of \(\Phi (R,A)\) (introduced in the paper). Necessary and sufficient conditions for a monounary algebra to be b-representable are found. In particular, every finite monounary algebra is b-representable.
Reviewer: I.Chajda (Olomouc)

MSC:
08A60 Unary algebras
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