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Nilpotent and solvable radicals in locally finite congruence modular varieties

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Abstract

The Loewy rank of a modular latticeL of finite height is defined as the leastn for which there exista 0=0<at, < ... <ar=1 inL such that each interval I[ai, ai+1] is a complemented lattice. In this paper, a generalized notion of Loewy rank is applied to obtain new results in the commutator theory of locally finite congruence modular varieties. LetV be a finitely generated congruence modular variety. We prove that every algebra inV has a largest nilpotent congruence and a largest solvable congruence. Moreover, there exist first order formulas which define these special congruences in every algebra ofV.

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Authors and Affiliations

  1. University of California at Berkeley, Berkeley, California, USA

    Ralph McKenzie

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  1. Ralph McKenzie
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Research supported by National Science Foundation Grant No. DMS-8302295.

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McKenzie, R. Nilpotent and solvable radicals in locally finite congruence modular varieties. Algebra Universalis 24, 251–266 (1987). https://doi.org/10.1007/BF01195264

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