A Family of Closed Classes in k-Valued Logic

Мещанинов, Д Г

doi:10.3103/s0278641919010059

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2020

2022

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“…For k = 3 such clones have been completely described by Bulatov in [4]. (See also Meshchaninov's paper [11].) Relying on this paper we are able to provide a complete description of the lattice I(p 3 ).…”

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confidence: 75%

Clones of Compatible Operations on Rings Z_{p^k}}

Ploščica,

Varga

2020

Preprint

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We investigate the lattice I(n) of clones on the ring Z n between the clone of polynomial functions and the clone of congruence preserving functions. The crucial case is when n is a prime power. For a prime p, the lattice I(p) is trivial and I(p 2 ) is known to be a 2-element lattice. We provide a description of I(p 3 ). To achieve this result, we prove a reduction theorem, which says that I(p k ) is isomorphic to a certain interval in the lattice of clones on Z p k−1 .

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confidence: 75%