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Displaying similar documents to “Pseudo B L -algebras and D R ℓ -monoids”

IF-filters of pseudo-BL-algebras

Magdalena Wojciechowska-Rysiawa (2015)

Discussiones Mathematicae - General Algebra and Applications

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Characterizations of IF-filters of a pseudo-BL-algebra are established. Some related properties are investigated. The notation of prime IF- filters and a characterization of a pseudo-BL-chain are given. Homomorphisms of IF-filters and direct product of IF-filters are studied.

On pseudo BE-algebras

Rajab Ali Borzooei, Arsham Borumand Saeid, Akbar Rezaei, Akefe Radfar, Reza Ameri (2013)

Discussiones Mathematicae - General Algebra and Applications

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In this paper, we introduce the notion of pseudo BE-algebra which is a generalization of BE-algebra. We define the concepts of pseudo subalgebras and pseudo filters and prove that, under some conditions, pseudo subalgebra can be a pseudo filter. We prove that every homomorphic image and pre-image of a pseudo filter is also a pseudo filter. Furthermore, the notion of pseudo upper sets in pseudo BE-algebras introduced and is proved that every pseudo filter is an union of pseudo upper sets. ...

A note on good pseudo BL-algebras

Magdalena Wojciechowska-Rysiawa (2010)

Discussiones Mathematicae - General Algebra and Applications

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Pseudo BL-algebras are a noncommutative extention of BL-algebras. In this paper we study good pseudo BL-algebras and consider some classes of these algebras.

Generalizations of pseudo MV-algebras and generalized pseudo effect algebras

Jan Kühr (2008)

Czechoslovak Mathematical Journal

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We deal with unbounded dually residuated lattices that generalize pseudo M V -algebras in such a way that every principal order-ideal is a pseudo M V -algebra. We describe the connections of these generalized pseudo M V -algebras to generalized pseudo effect algebras, which allows us to represent every generalized pseudo M V -algebra A by means of the positive cone of a suitable ℓ -group G A . We prove that the lattice of all (normal) ideals of A and the lattice of all (normal) convex ℓ -subgroups of...

Holland’s theorem for pseudo-effect algebras

Anatolij Dvurečenskij (2006)

Czechoslovak Mathematical Journal

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We give two variations of the Holland representation theorem for ℓ -groups and of its generalization of Glass for directed interpolation po-groups as groups of automorphisms of a linearly ordered set or of an antilattice, respectively. We show that every pseudo-effect algebra with some kind of the Riesz decomposition property as well as any pseudo M V -algebra can be represented as a pseudo-effect algebra or as a pseudo M V -algebra of automorphisms of some antilattice or of some linearly ordered...