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Article

Chajda, Ivan
Pseudocomplemented and Stone Posets. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 51 (2012), issue 1, pp. 29-34
MSC: 06A06, 06A11, 06D15 | MR 3060006 | Zbl 06204918
Keywords:
pseudocomplement; pseudocomplemented poset; Stone poset
Summary:
We show that every pseudocomplemented poset can be equivalently expressed as a certain algebra where the operation of pseudocomplementation can be characterized by means of remaining two operations which are binary and nullary. Similar characterization is presented for Stone posets.
References:
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[2] Frink, O.: Pseudo-complements in semi-lattices. Duke Math. J. 29 (1962), 505–514. DOI 10.1215/S0012-7094-62-02951-4 | MR 0140449 | Zbl 0114.01602
[3] Nimbhokar, S. K., Rahemani, A.: A note on Stone join-semilattices. Central European Journal of Math. 9 (2011), 929–933. DOI 10.2478/s11533-011-0031-1 | MR 2805325
[4] Venkatanarasimhan, P. V.: Pseudo-complements in posets. Proc. Amer. Math. Soc. 28 (1971), 9–17. DOI 10.1090/S0002-9939-1971-0272687-X | MR 0272687 | Zbl 0218.06002
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