Congruence pairs for algebras abstracting Kleene and Stone algebras

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چکیده

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Kleene and Stone Algebras

Boolean algebras are affine complete by a well-known result of G. Grätzer. Various generalizations of this result have been obtained. Among them, a characterization of affine complete Stone algebras having a smallest dense element was given by R. Beazer. In this paper, generalizations of Beazer’s result are presented for algebras abstracting simultaneously Kleene and Stone algebras.

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*-Continuous Kleene ω-Algebras

We define and study basic properties of ∗-continuous Kleene ω-algebras that involve a ∗-continuous Kleene algebra with a ∗-continuous action on a semimodule and an infinite product operation that is also ∗-continuous. We show that ∗-continuous Kleene ω-algebras give rise to iteration semiring-semimodule pairs. We show how our work can be applied to solve certain energy problems for hybrid systems.

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ژورنال

عنوان ژورنال: Czechoslovak Mathematical Journal

سال: 1985

ISSN: 0011-4642,1572-9141

DOI: 10.21136/cmj.1985.102014