Abstract.
We prove that if \({\mathbf{A}}\) is a finite algebra which satisfies a nontrivial idempotent Mal’cev condition, and if Con\({\mathbf{A}}\) contains a copy of an order polynomially complete lattice other than \({\mathbf{2}}\), \({\mathbf{M}}_{3}\), or Con\((\mathbb{Z}^{3}_{2})\), then Con\({\mathbf{A}}\) is not hereditary.
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Received March 7, 2006; accepted in final form December 5, 2006.
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Snow, J.W. OPC Lattices and Congruence Heredity. Algebra univers. 58, 59–71 (2008). https://doi.org/10.1007/s00012-008-2039-3
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DOI: https://doi.org/10.1007/s00012-008-2039-3