Congruences and Quotient Algebras of BCI-algebras

Yuzhong Ding; Zhiyong Pang

doi:10.2478/v10037-007-0021-8

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Congruences and Quotient Algebras of BCI-algebras

Formalized Mathematics

Volume 15 (2007): Issue 4 (December 2007)

By: Yuzhong Ding and Zhiyong Pang

Open Access

|Jun 2008

Abstract

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.

References

[1] Grzegorz Bancerek. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
Search in Google Scholar
[2] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
Search in Google Scholar
[3] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
Search in Google Scholar
[4] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
Search in Google Scholar
[5] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
Search in Google Scholar
[6] Yuzhong Ding. Several classes of BCI-algebras and their properties. Formalized Mathematics, 15(1):1-9, 2007.10.2478/v10037-007-0001-z
Search in Google Scholar
[7] Yisheng Huang. BCI-algebras. Science Press, 2006.
Search in Google Scholar
[8] Library Committee of the Association of Mizar Users. Binary operations on numbers. To appear in Formalized Mathematics.
Search in Google Scholar
[9] Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990.
Search in Google Scholar
[10] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.
Search in Google Scholar
[11] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.
Search in Google Scholar
[12] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
Search in Google Scholar
[13] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
Search in Google Scholar
[14] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
Search in Google Scholar
[15] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Formalized Mathematics, 1(1):85-89, 1990.
Search in Google Scholar