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Zbl 0842.08007
Chajda, I.
Normally presented varieties.
(English)
[J] Algebra Univers. 34, No.3, 327-335 (1995). ISSN 0002-5240; ISSN 1420-8911/e

An identity $p(x_1,\dots, x_n) = q(x_1,\dots, x_n)$ is called normal if it is of the form $x_1 = x_1$ or neither $p$ nor $q$ is a variable. For a variety $\cal V$, ${\cal N} ({\cal V})$ denotes the variety defined by all normal identities of $\cal V$. Let ${\germ A} \in {\cal V}$, $\Theta$ any congruence on $\germ A$ and $\kappa$ any function sending each $\Theta$ class to an element of the class and satisfying some non-triviality property. The author defines the choice algebras: For any $n$-ary term $f(x_1, \dots, x_n)$ and for elements $a_1, \dots, a_n$ let $f_{(\Theta,\kappa)} (a_1, \dots, a_n) = \kappa([f(a_1, \dots, a_n)]\Theta)$. The author proves that ${\cal N}({\cal V})$ consists of the homomorphic images of the choice algebras of the given variety. Some related questions and examples are discussed.
[E.Fried (Budapest)]
MSC 2000:
*08B99 Varieties of algebras

Keywords: normal identities; choice algebras

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