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Keywords:
Lattice effect algebra; CI-lattice; Sasaki arrow; (strong; fantastic; implicative; positive implicative) filter; Riesz ideal; D-ideal; MV-effect algebra; orthomodular lattice
Lattice effect algebra; CI-lattice; Sasaki arrow; (strong; fantastic; implicative; positive implicative) filter; Riesz ideal; D-ideal; MV-effect algebra; orthomodular lattice
Summary:
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.
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