\documentstyle[10pt]{article}
\author{\bf Bo\v{z}a Tasi\'{c} \\
Institute of Mathematics, Novi Sad, Yugoslavia\\}
\title{On operators in universal algebra and related structures}

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\begin{document}
\date{}
\maketitle
We will consider classes of algebras of the same type and operators on such
classes. Given a class $\cal K$ of algebras we let $I(\cal K)$ and $H(\cal
K)$ denote the classes of all isomorphic images and homomorphic images of
algebras in $\cal K$ respectively. Let $S(\cal K)$, $P(\cal K)$, $P_s(\cal
K)$, $P_u(\cal K)$, $P_f(\cal K)$, $R(\cal K)$ denote the class of all
algebras isomorphic to subalgebras, direct products, subdirect products,
ultraproducts, filtered products and retracts of algebras in $\cal K$
respectively. To the set of operators $\Sigma=\{I, R, H, S, P, P_s, P_u, P_f \}$
we can associate a different partially ordered semigroups (actually,
monoids) in a natural way. A well known result of this kind due to Pigozzi
appears in 1972. He describes the po-monoid ${\cal M}= \langle \tau
\rangle$ where $\tau =\{H, S, P\}$. ${\cal M}$ has eighteen elements
and the corresponding partial order is given by Figure below.
The aim of this talk is to present known results of this kind.
Partially ordered monoids generated by the folowing subsets of $\Sigma$:
$\theta =\{H, S, P, P_s\}$, $\varphi =\{R, H, S, P\}$, $\tau =\{H, S, P,
P_f\}$, $\psi =\{H, S, P_u\}$, $\rho =\{H, S, P_f\}$, and other
will be disscussed.

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