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Nonstandard subdirect representations in axiomatizable classes. (English. Russian original) Zbl 0577.08008

Sib. Math. J. 25, 347-360 (1984); translation from Sib. Mat. Zh. 25, No. 3(145), 14-29 (1984).
From the authors’ introduction: In this article, we introduce and investigate three variants of nonstandard subdirect representations in axiomatizable classes of algebraic systems, in each of which the compositions \(\pi_ i\cdot \mu\) [where \(\mu : A\to \prod A_ j\) is the representing embedding and \(\pi_ i: \prod A_ j\to A_ i\) is the \(i\)th projection] are subjected, besides the Burris condition [S. Burris, Colloq. Math. 34, 191–197 (1976; Zbl 0326.08005)] (“of being a strong homomorphism”), also to a condition, formulated in terms of a system of axioms, defining the class.
Reviewer: E.Nelson

MSC:

08C10 Axiomatic model classes
08A05 Structure theory of algebraic structures
03C52 Properties of classes of models

Citations:

Zbl 0326.08005
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References:

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