Displaying similar documents to “Remarks on congruence relations and weak automorphisms in abstract algebras”

On weak automorphisms of universal algebras

R. James

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CONTENTSIntroduction.................................................................................................................... 5Section 1. The group of weak automorphisms...................................................... 6Section 2. Weak automorphisms of finitely generated free algebras................ 9Section 3. Representation of groups as weak automorphism groups ofalgebras............................................................................................................................

Implication algebras

Ivan Chajda (2006)

Discussiones Mathematicae - General Algebra and Applications

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We introduce the concepts of pre-implication algebra and implication algebra based on orthosemilattices which generalize the concepts of implication algebra, orthoimplication algebra defined by J.C. Abbott [2] and orthomodular implication algebra introduced by the author with his collaborators. For our algebras we get new axiom systems compatible with that of an implication algebra. This unified approach enables us to compare the mentioned algebras and apply a unified treatment of congruence...

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.

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...

Subalgebras and homomorphic images of algebras having the CEP and the WCIP

Andrzej Walendziak (2004)

Czechoslovak Mathematical Journal

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In the present paper we consider algebras satisfying both the congruence extension property (briefly the CEP) and the weak congruence intersection property (WCIP for short). We prove that subalgebras of such algebras have these properties. We deduce that a lattice has the CEP and the WCIP if and only if it is a two-element chain. We also show that the class of all congruence modular algebras with the WCIP is closed under the formation of homomorphic images.