Generalized "Boolean" theory of universal algebras. Part I.
Alfred L. Foster (1953)
Mathematische Zeitschrift
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Displaying similar documents to “On the representation of Boolean algebras as fields of sets”
Generalized "Boolean" theory of universal algebras. Part I.
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Generalized "Boolean" theory of universal algebras. Part II. Identities and subdirect sums of functionally complete algebras.
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On Algebras for which Every Faithful Representation is its Own Second Commutator.
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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.
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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).