Quotient structures in lattice effect algebras

Amir Hossein Sharafi; Rajb Ali Borzooei

Kybernetika (2019)

  • Volume: 55, Issue: 5, page 879-895
  • ISSN: 0023-5954

Abstract

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In this paper, we define some types of filters in lattice effect algebras, investigate some relations between them and introduce some new examples of lattice effect algebras. Then by using the strong filter, we find a CI-lattice congruence on lattice effect algebras, such that the induced quotient structure of it is a lattice effect algebra, too. Finally, under some suitable conditions, we get a quotient MV-effect algebra and a quotient orthomodular lattice, by this congruence relation.

How to cite

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Sharafi, Amir Hossein, and Borzooei, Rajb Ali. "Quotient structures in lattice effect algebras." Kybernetika 55.5 (2019): 879-895. <http://eudml.org/doc/295061>.

@article{Sharafi2019,
abstract = {In this paper, we define some types of filters in lattice effect algebras, investigate some relations between them and introduce some new examples of lattice effect algebras. Then by using the strong filter, we find a CI-lattice congruence on lattice effect algebras, such that the induced quotient structure of it is a lattice effect algebra, too. Finally, under some suitable conditions, we get a quotient MV-effect algebra and a quotient orthomodular lattice, by this congruence relation.},
author = {Sharafi, Amir Hossein, Borzooei, Rajb Ali},
journal = {Kybernetika},
keywords = {Lattice effect algebra; CI-lattice; Sasaki arrow; (strong; fantastic; implicative; positive implicative) filter; Riesz ideal; D-ideal; MV-effect algebra; orthomodular lattice},
language = {eng},
number = {5},
pages = {879-895},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Quotient structures in lattice effect algebras},
url = {http://eudml.org/doc/295061},
volume = {55},
year = {2019},
}

TY - JOUR
AU - Sharafi, Amir Hossein
AU - Borzooei, Rajb Ali
TI - Quotient structures in lattice effect algebras
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 5
SP - 879
EP - 895
AB - In this paper, we define some types of filters in lattice effect algebras, investigate some relations between them and introduce some new examples of lattice effect algebras. Then by using the strong filter, we find a CI-lattice congruence on lattice effect algebras, such that the induced quotient structure of it is a lattice effect algebra, too. Finally, under some suitable conditions, we get a quotient MV-effect algebra and a quotient orthomodular lattice, by this congruence relation.
LA - eng
KW - Lattice effect algebra; CI-lattice; Sasaki arrow; (strong; fantastic; implicative; positive implicative) filter; Riesz ideal; D-ideal; MV-effect algebra; orthomodular lattice
UR - http://eudml.org/doc/295061
ER -

References

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