Abstract
In this paper, we characterize the congruence lattice of a symmetric extended De Morgan algebra \(L\). We show that the congruence lattice of the algebra \(L\) is a pseudocomplemented lattice, and that such a congruence lattice is a Stone lattice if and only if the lattice of the compact congruences on \(L\) forms a complete Boolean lattice. In particular, we prove that the congruence lattice of \(L\) is a Boolean lattice if and only if, it is a relative Stone lattice, which is the case, if and only if \(L\) is finite.
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Supposed by the Natural Science Foundation of China (No. 11261021) is gratefully acknowledged.
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Communicated by Kar Ping Shum.
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Fang, J., Wang, LB. Congruence Lattices of Symmetric Extended De Morgan Algebras. Bull. Malays. Math. Sci. Soc. 38, 1471–1480 (2015). https://doi.org/10.1007/s40840-014-0084-y
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DOI: https://doi.org/10.1007/s40840-014-0084-y