Principal congruences of pseudocomplemented semilattices and congruence extension property

Sankappanavar, H. P.

doi:10.1090/S0002-9939-1979-0518510-4

Principal congruences of pseudocomplemented semilattices and congruence extension property
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by H. P. Sankappanavar

Proc. Amer. Math. Soc. 73 (1979), 308-312

DOI: https://doi.org/10.1090/S0002-9939-1979-0518510-4

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Abstract:

Principal congruences of pseudocomplemented semilattices are characterized and shown to be definable. This characterization is then applied to give a new proof of the fact that the variety of pseudocomplemented semilattices has the congruence extension property.

References

John T. Baldwin and Joel Berman, The number of subdirectly irreducible algebras in a variety, Algebra Universalis 5 (1975), no. 3, 379–389. MR 392765, DOI 10.1007/BF02485271
Raymond Balbes and Alfred Horn, Stone lattices, Duke Math. J. 37 (1970), 537–545. MR 277448
Alan Day, A note on the congruence extension property, Algebra Universalis 1 (1971/72), 234–235. MR 294215, DOI 10.1007/BF02944983
R. A. Dean and Robert H. Oehmke, Idempotent semigroups with distributive right congruence lattices, Pacific J. Math. 14 (1964), 1187–1209. MR 172939
Orrin Frink, Pseudo-complements in semi-lattices, Duke Math. J. 29 (1962), 505–514. MR 140449
E. Fried and G. Grätzer, A nonassociative extension of the class of distributive lattices, Pacific J. Math. 49 (1973), 59–78. MR 340128
G. Grätzer and H. Lakser, The structure of pseudocomplemented distributive lattices. II. Congruence extension and amalgamation, Trans. Amer. Math. Soc. 156 (1971), 343–358. MR 274359, DOI 10.1090/S0002-9947-1971-0274359-9

Pseudocomplemented semilattices

Harry Lakser, Principal congruences of pseudocomplemented distributive lattices, Proc. Amer. Math. Soc. 37 (1973), 32–36. MR 392730, DOI 10.1090/S0002-9939-1973-0392730-9

A study of congruence lattices of pseudocomplemented semilattices