Geodesic
Some p-algebras and double p-algebras having only principal congruences
Glasgow mathematical journal, Tome 34 (1992) no. 2, pp. 157-164

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In [6], Blyth and Varlet characterize those algebras having only principal congruences in some well known classes of algebras having distributive lattice reducts. In particular, they characterize those Stone algebras having only principal congruences. In this paper we characterize those quasi-modular p-algebras having only principal congruences and show on specializing that distributive p-algebras having only principal congruences can be described in exactly the same way as Blyth and Varlet described Stone algebras having the same property. The same problem is addressed for some distributive double p-algebras. 
Beazer, R. Some p-algebras and double p-algebras having only principal congruences. Glasgow mathematical journal, Tome 34 (1992) no. 2, pp. 157-164. doi: 10.1017/S0017089500008673
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