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Journal of Mathematics and Applications

Journal of Mathematics and Applications
4/36, DOI: 10.7862/rf.2013.4

On duality between order and algebraic structures in Boolean systems

Aneta Dadej, Katarzyna Halik

DOI: 10.7862/rf.2013.4

Abstract

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.

Full text (pdf)

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About this Article

TITLE:
On duality between order and algebraic structures in Boolean systems

AUTHORS:
Aneta Dadej (1)
Katarzyna Halik (2)

AUTHORS AFFILIATIONS:
(1) .Institute of Mathematics,
University of Rzeszow,
ul. Rejtana 16A,
35-310 Rzeszow, Poland.. (afiliacja nr 1 dla Aneta Dadej)
... (afiliacja nr 2 dla Aneta Dadej)
...
(2) Institute of Mathematics,
University of Rzeszow,
ul. Rejtana 16A,
35-310 Rzeszow, Poland... (afiliacja nr 1 dla Katarzyna Halik)
... (afiliacja nr 2 dla Katarzyna Halik)
...

JOURNAL:
Journal of Mathematics and Applications
4/36

KEY WORDS AND PHRASES:
lattice, 0-lattice, join-semilattice, 0-join-semilattice, distribu-tive 0-lattice, B-ring, Delta-join-semilattices, Boolean algebra, algebraic ring, Boolean ring

FULL TEXT:
http://doi.prz.edu.pl/pl/pdf/jma/12

DOI:
10.7862/rf.2013.4

URL:
http://dx.doi.org/10.7862/rf.2013.4

RECEIVED:
2013-03-12

REVISITED:
2013-08-25

COPYRIGHT:
Oficyna Wydawnicza Politechniki Rzeszowskiej, al. Powstańców Warszawy 12, 35-959 Rzeszów

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