Non-covering in the interpretability lattice of equational theories.

*(English)*Zbl 0802.08004This 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.

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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\textit{R. McKenzie} and \textit{S. Świerczkowski}, Algebra Univers. 30, No. 2, 157--170 (1993; Zbl 0802.08004)

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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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