The lattice of monomial clones on finite fields
AbstractWe investigate the lattice of clones that are generated by a set of functions that are induced on a finite field $${\mathbb {F}}$$ F by monomials. We study the atoms and coatoms of this lattice and investigate whether this lattice contains infinite ascending chains, or infinite descending chains, or infinite antichains.We give a connection between the lattice of these clones and semi-affine algebras. Furthermore, we show that the sublattice of idempotent clones of this lattice is finite and every idempotent monomial clone is principal.
2012 ◽
Vol 55
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pp. 418-423
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2003 ◽
Vol 55
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pp. 225-246
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2020 ◽
Vol 31
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pp. 411-419
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2016 ◽
Vol 12
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pp. 1519-1528
2016 ◽
Vol 161
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pp. 469-487
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1970 ◽
Vol 11
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pp. 21-36
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