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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
##### Keywords:
bottleneck algebra; monounary algebra; b-representability
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