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Non-covering in the interpretability lattice of equational theories. (English) Zbl 0802.08004
This is a very well-written paper, a delightful reading, even for people who are not familiar with the topic. The authors prove some results on balanced equational theories. As a corollary, they present a large class of equational theories which have no covering equational theories (up to equivalence of theories in a natural sense).
To go into details would need quite a few definitions and observations. Instead I recommend to read this important paper.
Reviewer: E.Fried (Budapest)

MSC:
08B05 Equational logic, Mal’tsev conditions
03C05 Equational classes, universal algebra in model theory
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References:
[1] Garcia, O. andTaylor, W.,The lattice of interpretability types of varieties, AMS Memoirs No.305 (1984). · Zbl 0559.08003
[2] McKenzie, R.,On the covering relation in the interpretability lattice of equational theories, Algebra Universalis (to appear). · Zbl 0802.08005
[3] McKenzie R. andTaylor W.,Interpretations of module varieties, Journal of Algebra135 (1990), 456–493. · Zbl 0729.08005
[4] Mycielski J. andTaylor, W.,Remarks and problems on a lattice of equaional chapters, Algebra Universalis23 (1986), 24–31. · Zbl 0616.08014
[5] Taylor, W.,Some very weak identities, Algebra Universalis25 (1988), 27–35. · Zbl 0646.08004
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