Displaying similar documents to “Congruences, ideals and annihilators in standard QBCC-algebras”

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...

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.