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Keywords:
MS-algebra; permutable congruence; congruence system
MS-algebra; permutable congruence; congruence system
Summary:
Let $L$ be an MS-algebra with congruence permutable skeleton. We prove that solving a system of congruences $(\theta _{1},\ldots ,\theta _{n};x_{1} ,\ldots ,x_{n})$ in $L$ can be reduced to solving the restriction of the system to the skeleton of $L$, plus solving the restrictions of the system to the intervals $[x_{1},\bar{\bar{x}}_{1}],\dots ,[x_{n},\bar{ \bar{x}}_{n}].$
References:
[1] R. Balbes, P. Dwinger: Distributive Lattices. University of Missouri Press, Columbia, Missouri, 1974. MR 0373985
[2] T. S. Blyth, J. C. Varlet: Ockham Algebras. Oxford University Press, 1994. MR 1315526
[3] H. Gramaglia, D. Vaggione: Birkhoff-like sheaf representation for varieties of lattice expansions. Studia Logica 56 (1996), 111–131. DOI 10.1007/BF00370143 | MR 1382170
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