Random Models of Idempotent Linear Maltsev Conditions. I. Idemprimality

DOI10.1007/S00012-019-0636-YarXiv1901.06316MaRDI QIDQ6312686

Clifford Bergman, Ágnes Szendrei

Publication date: 18 January 2019

Abstract: We extend a well-known theorem of Murskiv{i} to the probability space of finite models of a system $mathcalM$ of identities of a strong idempotent linear Maltsev condition. We characterize the models of $mathcalM$ in a way that can be easily turned into an algorithm for producing random finite models of $mathcalM$, and we prove that under mild restrictions on $mathcalM$, a random finite model of $mathcalM$ is almost surely idemprimal. This implies that even if such an $mathcalM$ is distinguishable from another idempotent linear Maltsev condition by a finite model $mathbfA$ of $mathcalM$, a random search for a finite model $mathbfA$ of $mathcalM$ with this property will almost surely fail.

Mathematics Subject Classification ID

Equational logic, Mal'tsev conditions (08B05) Operations and polynomials in algebraic structures, primal algebras (08A40)

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