Abstract
A characterization of the congruence lattice of a principal p-algebra satisfying a certain condition in terms of congruence pairs is given.
Acknowledgement
The author would like to thank the referee for his valuable comments and suggestions to improve this presentation.
References
[1] Badawy, A.—Shum, K. P.: Congruences and Boolean filters of quasi-modular p-algebras, Discuss. Math. Gen. Algebra Appl. 34 (2014), 109–123.10.7151/dmgaa.1212Search in Google Scholar
[2] Badawy, A.—Shum, K. P.: Congruence pairs of principal p-algebras, Math. Slovaca 67 (2017), 263–270.10.1515/ms-2016-0265Search in Google Scholar
[3] Badawy, A.—Atallah, M.: Boolean filters of principal p-algebras, Int. J. Math. Comput. 26, (2015), 15–25.Search in Google Scholar
[4] Badawy, A.: Congruences and d-filters of principal p-algebras, J. Egyptian Math. Soc. 24 (2016), 160–164.10.1016/j.joems.2015.04.003Search in Google Scholar
[5] Badawy, A.: Filters of p-algebras with respect to a closure operator, Southeast Asian Bull. Math. 40 (2016), 37–47.Search in Google Scholar
[6] Birkhoff, G.: Lattice Theory, Colloquium Publications, Amer. Math. Soc., New York, 1967.Search in Google Scholar
[7] El-Assar, S.: Two notes on the congruence lattice of the p-algebras, Acta Math. Univ. Comenian. 66-67 (1985), 13–19.Search in Google Scholar
[8] Birkhoff, G.—Schmidt, E. T.: Ideals and congruence relations in lattices, Acta Math. Hungar. 9 (1958), 137–175.10.1007/BF02023870Search in Google Scholar
[9] Grätzer, G.: Lattice Theory: First Concepts and Distributive Lattices, Freeman, San Francisco, California, 1971.Search in Google Scholar
[10] Haviar, M. Construction and affine completeness of principal p-algebras, Tatra Mt. Math. Publ. 5 (1995), 217–228.Search in Google Scholar
[11] Katriňák, T.: On a problem of G. Grätzer, Proc. Amer. Math. Soc. 1 (1976), 19–24.10.1090/S0002-9939-1976-0401593-7Search in Google Scholar
[12] Katriňák, T.—Mederly, P.: Construction of modular p-algebras, Algebra Universalis 4 (1974), 301–310.10.1007/BF02485742Search in Google Scholar
© 2017 Mathematical Institute Slovak Academy of Sciences
