Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Principal congruences of $ p$-algebras and double $ p$-algebras


Authors: T. Hecht and T. Katriňák
Journal: Proc. Amer. Math. Soc. 58 (1976), 25-31
MSC: Primary 06A25
DOI: https://doi.org/10.1090/S0002-9939-1976-0409293-4
MathSciNet review: 0409293
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Principal congruence of pseudocomplemented lattices (= $ p$-algebras) and of double pseudocomplemented lattices (= double $ p$-algebras), i.e. pseudocomplemented and dual pseudocomplemented ones, are characterized.


References [Enhancements On Off] (What's this?)

  • [1] A. Day, A note on the congruence extension property, Algebra Universalis 1 (1971/72), 234-235. MR 45 #3288. MR 0294215 (45:3288)
  • [2] G. Grätzer, Universal algebra, Van Nostrand, Princeton, N.J., 1968. MR 40 #1320. MR 0248066 (40:1320)
  • [3] -, Lattice theory. First concepts and distributive lattices, Freeman, San Francisco, Calif., 1971. MR 48 #184. MR 0321817 (48:184)
  • [4] T. Katriňák, Primitive Klassen von modularen $ S$-Algebren, J. Reine Angew. Math. 261 (1973), 55-70. MR 0392725 (52:13542)
  • [5] -, Congruence extension property for distributive double $ p$-algebras, Algebra Univervalis 4 (1974), 273-276. MR 50 #6953. MR 0354475 (50:6953)
  • [6] -, Construction of regular double $ p$-algebras, Bull. Soc. Roy. Sci. Liège 43 (1974), 283-290. MR 0373984 (51:10184)
  • [7] H. Lakser, Principal congruences of pseudocomplemented distributive lattices, Proc. Amer. Math. Soc. 37 (1973), 32-36. MR 0392730 (52:13547)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06A25

Retrieve articles in all journals with MSC: 06A25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0409293-4
Keywords: $ p$-algebra, dual $ p$-algebra, double $ p$-algebra, distributive $ p$-algebra, distributive double $ p$-algebra, Boolean algebra, pseudocomplement, dual pseudocomplement, closed element, principal congruence, principal lattice congruence
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society