On duality between order and algebraic structures in Boolean systems

• Autorzy: Dadej A. , Halik K.

Identyfikatory

DOI

10.7862/rf.2013.4

• Języki publikacji: EN

Abstrakty

EN

We present an extension of the known one-to-one correspondence between Boolean algebras and Boolean rings with unit being two types of Boolean systems endowed with order and algebraic structures, respectively. Two equivalent generalizations of Boolean algebras are discussed. We show that there is a one-to-one correspondence between any of the two mentioned generalized Boolean algebras and Boolean rings without unit.

Słowa kluczowe

EN

lattice; 0-lattice; join-semilattice; 0-join-semilattice; distributive 0-lattice; B-ring; ∆-join-semilattices; Boolean algebra; algebraic ring; Boolean ring

PL

algebra Boole'a; pierścień Boole'a; krata

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2013
• Tom: Vol. 36
• Strony: 35--62
• Opis fizyczny: Bibliogr. 45 poz.

Twórcy

autor

Dadej A.

• Institute of Mathematics, University of Rzeszow, ul. Rejtana 16A, 35-310 Rzeszow, Poland

autor

Halik K.

• Institute of Mathematics, University of Rzeszow, ul. Rejtana 16A, 35-310 Rzeszow, Poland

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