Displaying similar documents to “Implication algebras”

On GE-algebras

Ravikumar Bandaru, Arsham Borumand Saeid, Young Bae Jun (2021)

Bulletin of the Section of Logic

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Hilbert algebras are important tools for certain investigations in intuitionistic logic and other non-classical logic and as a generalization of Hilbert algebra a new algebraic structure, called a GE-algebra (generalized exchange algebra), is introduced and studied its properties. We consider filters, upper sets and congruence kernels in a GE-algebra. We also characterize congruence kernels of transitive GE-algebras.

Congruence submodularity

Ivan Chajda, Radomír Halaš (2002)

Discussiones Mathematicae - General Algebra and Applications

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We present a countable infinite chain of conditions which are essentially weaker then congruence modularity (with exception of first two). For varieties of algebras, the third of these conditions, the so called 4-submodularity, is equivalent to congruence modularity. This is not true for single algebras in general. These conditions are characterized by Maltsev type conditions.

Congruences and Quotient Algebras of BCI-algebras

Yuzhong Ding, Zhiyong Pang (2007)

Formalized Mathematics

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We have formalized the BCI-algebras closely following the book [7] pp. 16-19 and pp. 58-65. Firstly, the article focuses on the properties of the element and then the definition and properties of congruences and quotient algebras are given. Quotient algebras are the basic tools for exploring the structures of BCI-algebras.

On congruence distributivity of ordered algebras with constants

Krisztina Balog, Benedek Skublics (2011)

Discussiones Mathematicae - General Algebra and Applications

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We define the order-congruence distributivity at 0 and order- congruence n-distributivity at 0 of ordered algebras with a nullary operation 0. These notions are generalizations of congruence distributivity and congruence n-distributivity. We prove that a class of ordered algebras with a nullary operation 0 closed under taking subalgebras and direct products is order-congruence distributive at 0 iff it is order-congruence n-distributive at 0. We also characterize such classes by a Mal'tsev...