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On Birkhoff's Problem 73 For Monoids
Published online by Cambridge University Press: 20 November 2018
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Birkhoff in [2] poses the following problem:
“Problem 73. Find necessary and sufficient conditions in order that the correspondence between the congruence relations and the (neutral) ideals of a lattice be one-one”.
This problem has been solved by Areškin [l] and Hashimoto [3]. Essentially the conditions reduce to the r e quirement that the lattice be a generalized Boolean algebra.
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