论文标题
有限场上单个克隆的晶格
The lattice of monomial clones on finite fields
论文作者
论文摘要
我们调查了由单个单位诱导的一组函数生成的克隆晶格，这些函数$ \ mathbb {f} $由Monomials诱导。我们研究了该晶格的原子和外套，并研究了该晶格是否包含无限上升的链，无限的降链或无限的抗敌。我们在这些克隆的晶格和半植物代数之间提供了联系。此外，我们表明，该格隆的diDempotent克隆的sublattice是有限的，每个愿意的单一单元克隆都是主要的。
We investigate the lattice of clones that are generated by a set of functions that are induced on a finite field $\mathbb{F}$ 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.
