Displaying similar documents to “Generalized 'Boolean' theory of universal algebras. Part I.”

Two constructions of De Morgan algebras and De Morgan quasirings

Ivan Chajda, Günther Eigenthaler (2009)

Discussiones Mathematicae - General Algebra and Applications

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De Morgan quasirings are connected to De Morgan algebras in the same way as Boolean rings are connected to Boolean algebras. The aim of the paper is to establish a common axiom system for both De Morgan quasirings and De Morgan algebras and to show how an interval of a De Morgan algebra (or De Morgan quasiring) can be viewed as a De Morgan algebra (or De Morgan quasiring, respectively).

The elementary-equivalence classes of clopen algebras of P-spaces

Brian Wynne (2008)

Fundamenta Mathematicae

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Two Boolean algebras are elementarily equivalent if and only if they satisfy the same first-order statements in the language of Boolean algebras. We prove that every Boolean algebra is elementarily equivalent to the algebra of clopen subsets of a normal P-space.

A common approach to directoids with an antitone involution and D-quasirings

Ivan Chajda, Miroslav Kolařík (2008)

Discussiones Mathematicae - General Algebra and Applications

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We introduce the so-called DN-algebra whose axiomatic system is a common axiomatization of directoids with an antitone involution and the so-called D-quasiring. It generalizes the concept of Newman algebras (introduced by H. Dobbertin) for a common axiomatization of Boolean algebras and Boolean rings.