Essential extensions of stone algebras

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1977 English Publisher:Springer Science and Business Media LLCJournal:Algebra Universalis, volume 7, pages 1-3 (issn: 0002-5270, eissn: 1420-8911,

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Authors: Katriňák, Tibor;

doi: 10.1007/bf02485413

Essential extensions of stone algebras

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Abstract

A distributive \(p\)-algebra \(\langle L;\cup,\cap,*,0,1\rangle\) (see the review of [the author, Algebra Univers. 7, 265--271 (1977; Zbl 0358.06026)]) is called a Stone algebra if \(L\) satisfies the identity \(x^*\cup x^{**} =1\). In the paper the essential extensions of Stone algebras are characterized, which improves an earlier result of \textit{H. Lakser} [Proc. Am. Math. Soc. 24, 524--529 (1970; Zbl 0191.31504)].

Keywords

Pseudocomplemented lattices, Structure and representation theory of distributive lattices

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