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Essential extensions of stone algebras
Algebra Universalis, 1977A 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.
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2017
We study a generalisation of relation algebras in which the underlying Boolean algebra structure is replaced with a Stone algebra. Many theorems of relation algebras generalise with no or small changes. Weighted graphs represented as matrices over extended real numbers form an instance.
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We study a generalisation of relation algebras in which the underlying Boolean algebra structure is replaced with a Stone algebra. Many theorems of relation algebras generalise with no or small changes. Weighted graphs represented as matrices over extended real numbers form an instance.
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On the Triple Characterization for Stone Algebras
Canadian Journal of Mathematics, 1975In [1], C. C. Chen and G. Grâtzer developed a method for studying Stone algebras by associating with each Stone algebra L, a uniquely determined triple (C(L), D(L), ɸ (L)), consisting of a Boolean algebra C(L), a distributive lattice D(L), and a connecting map ɸ(L).
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Quantifier elimination for Stone algebras
Archive for Mathematical Logic, 1989A Stone algebra is a distributive lattice with pseudocomplement that satisfies the Stone identity \(a^*\sqcup a^{**}=1\). The author determines all quantifier elimination classes of Stone algebras and all classes of Stone algebras that admit positive quantifier elimination (i.e.
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Priestley Duality for Quasi-Stone Algebras
Studia Logica, 2000The author describes the Priestley space of a quasi-Stone algebra in terms of a Priestley space with a certain equivalence relation. He shows that finite quasi-Stone algebras enjoy the amalgamation property and describes the Priestley space for free quasi-Stone algebras over a finite set.
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De Morgan Algebras with a Quasi-Stone Operator
Studia Logica, 2013In this work, the class of those algebras \((L;^{\circ} ,^{\ast})\) is investigated where \((L;^{\circ})\) is a De Morgan algebra, \((L;^{\ast})\) is a quasi-Stone algebra, and the unary operations \(x\longrightarrow x^{\circ}\) and \(x\longrightarrow x^{\ast}\) satisfy the identity \(x^{\ast\ast\circ}=x^{\ast\circ\ast}\).
T. S. Blyth, Jie Fang, Lei-Bo Wang
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Affine complete Stone algebras
Algebra Universalis, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Haviar, M., Ploščica, M.
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Post-like algebras and injective Stone algebras
Algebra Universalis, 1975In [3] Balbes and Grw gave intrinsic and extrinsic characterizations of injective Stone algebras. Specifically, the injectives can be characterized (extrinsically) as those Stone algebras that are the direct product of a complete Boolean algebra with a complete Post algebra of order three.
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What makes a Stone topological algebra Profinite
Algebra Universalis, 2023Jorge Almeida +2 more
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