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Finiteness of semigroups of operators in universal algebra. (English) Zbl 0149.26004

Let \(H, S, P, P_S, P_F, P_U, C\) be operators on classes of universal algebras corresponding to homomorphic images, subalgebras, direct products, subdirect products, filter products, ultra products and covers, respectively. Then the partially ordered semigroups generated by the following sets of operators are finite: \(\{H, S, P, P_S\}\), \(\{C, H, S, P, P_F\}\), \(\{C, H, S, P_F, P_U\}\).
Reviewer: E. Nelson

MSC:

08-XX General algebraic systems
06F05 Ordered semigroups and monoids
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