Dietlinde Lau
Congruences on closed subsets of $\widetilde{P_k}$ and of $P_{k,L}$
The paper is published: Rostocker Mathematische Kolloquium, Rostock. Math. Kolloq. 48, 19-26 (1995)
MSC:
08A40 Operations, polynomials, primal algebras
Abstract: Let be $E_k:=\{0,1,\ldots ,k-1\},\ k\geq 2,\ P_k:=\bigcup_{n\geq 1}P^n_k,\ P^n_k :=\{f^n|f^n:E^n_k\rightarrow E_k\}$ and $\text{\boldmath{$P_k$}}:=(P_k;\zeta,\ta u,\triangle,\nabla,*)$,
where $\zeta,\ \tau,\ \triangle,\ \nabla,\ *$ denote the Mal'cev operations on $P_k$ (see [6] or [7]).
If the arity $n$ of $f^n$ can be seen from the context, we omit the upper
index.
\bs
Here we consider the algebras
$\text{\boldmath{P(i)}}\ :=\ (P(i),\Omega_i)$
as a generalization of {\boldmath$P_k$} with $i\ \in\ \{0,1,2\}$,\\
$P(0) := \widetilde{P_k} =\bigcup_{n\geq 1}\widetilde{P_k^n},\ \widetilde{P_k^n}\ :=\{f^n|f^n:E^n_k\right arrow E_k\cup\{\infty\}\}$,\\
$P(1)=P(2):=P_{k,L}=\bigcup_{n\geq 1}P^n_{k,L},\ P^n_{k,L}:=\{f^n|f^n:E^n_k\righ tarrow E_L\}$\\
for $L>k$ and
$\Omega_i:=\{\zeta,\tau,\triangle,\nabla,*_i\}$.
Notes: Abstract contains the first few lines of text of the paper.