Displaying similar documents to “Irredundant Decomposition of Algebras into One-Dimensional Factors”

Quotient structures in lattice effect algebras

Amir Hossein Sharafi, Rajb Ali Borzooei (2019)

Kybernetika

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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. ...

Decomposition of Congruence Modular Algebras into Atomic, Atomless Locally Uniform and Anti-Uniform Parts

Bogdan Staruch, Bożena Staruch (2016)

Bulletin of the Section of Logic

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We describe here a special subdirect decomposition of algebras with modular congruence lattice. Such a decomposition (called a star-decomposition) is based on the properties of the congruence lattices of algebras. We consider four properties of lattices: atomic, atomless, locally uniform and anti-uniform. In effect, we describe a star-decomposition of a given algebra with modular congruence lattice into two or three parts associated to these properties.

Normalization of basic algebras

Miroslav Kolařík (2008)

Discussiones Mathematicae - General Algebra and Applications

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We consider algebras determined by all normal identities of basic algebras. For such algebras, we present a representation based on a q-lattice, i.e., the normalization of a lattice.

Atomicity of lattice effect algebras and their sub-lattice effect algebras

Jan Paseka, Zdena Riečanová (2009)

Kybernetika

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We show some families of lattice effect algebras (a common generalization of orthomodular lattices and MV-effect algebras) each element E of which has atomic center C(E) or the subset S(E) of all sharp elements, resp. the center of compatibility B(E) or every block M of E. The atomicity of E or its sub-lattice effect algebras C(E), S(E), B(E) and blocks M of E is very useful equipment for the investigations of its algebraic and topological properties, the existence or smearing of states...

Classification systems and their lattice

Sándor Radeleczki (2002)

Discussiones Mathematicae - General Algebra and Applications

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We define and study classification systems in an arbitrary CJ-generated complete lattice L. Introducing a partial order among the classification systems of L, we obtain a complete lattice denoted by Cls(L). By using the elements of the classification systems, another lattice is also constructed: the box lattice B(L) of L. We show that B(L) is an atomistic complete lattice, moreover Cls(L)=Cls(B(L)). If B(L) is a pseudocomplemented lattice, then every classification system of L is independent...

Weak congruences of an algebra with the CEP and the WCIP

Andrzej Walendziak (2002)

Czechoslovak Mathematical Journal

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Here we consider the weak congruence lattice C W ( A ) of an algebra A with the congruence extension property (the CEP for short) and the weak congruence intersection property (briefly the WCIP). In the first section we give necessary and sufficient conditions for the semimodularity of that lattice. In the second part we characterize algebras whose weak congruences form complemented lattices.