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sectionally pseudocomplemented semilattice; weakly standard element
Sectionally pseudocomplemented semilattices are an extension of relatively pseudocomplemented semilattices—they are meet-semilattices with a greatest element such that every section, i.e., every principal filter, is a pseudocomplemented semilattice. In the paper, we give a simple equational characterization of sectionally pseudocomplemented semilattices and then investigate mainly their congruence kernels which leads to a characterization of subdirectly irreducible sectionally pseudocomplemented semilattices.
[1] S. Burris and H. P. Sankappanavar: A Course in Universal Algebra. Springer Verlag, New York, 1981. MR 0648287
[2] I. Chajda: An extension of relative pseudocomplementation to non-distributive lattices. Acta Sci. Math. (Szeged) 69 (2003), 491–496. MR 2034188 | Zbl 1048.06005
[3] I. Chajda, G. Eigenthaler and H. Länger: Congruence Classes in Universal Algebra. Heldermann Verlag, Lemgo, 2003. MR 1985832
[4] I. Chajda and R. Halaš: Sectionally pseudocomplemented lattices and semilattices. In: K. P. Shum (ed.) et al., Advances in Algebra. Proceedings of the ICM sattelite conference in algebra and related topics, Hong Kong, China, August 14–17, 2002. World Scientific, River Edge. 2003, pp. 282–290. MR 2088449
[5] I. Chajda and S. Radeleczki: On varieties defined by pseudocomplemented nondistributive lattices. Publ. Math. Debrecen 63 (2003), 737–750. MR 2020784
[6] G. Grätzer: General Lattice Theory (2nd edition). Birkhäuser Verlag, Basel-Boston-Berlin, 1998. MR 1670580
[7] P. Köler: Brouwerian semilattices. Trans. Amer. Math. Soc. 268 (1981), 103–126. DOI 10.1090/S0002-9947-1981-0628448-3 | MR 0628448
[8] W. C. Nemitz: Implicative semi-lattices. Trans. Amer. Math. Soc. 117 (1965), 128–142. DOI 10.1090/S0002-9947-1965-0176944-9 | MR 0176944 | Zbl 0128.24804
[9] J. C. Varlet: A generalization of the notion of pseudo-complementedeness. Bull. Soc. Roy. Liège 37 (1968), 149–158. MR 0228390
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