Congruences and Quotient Algebras of BCI-algebras
Yuzhong Ding ; Zhiyong Pang
Formalized Mathematics, Tome 15 (2007), p. 175-180 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:267323 
@article{bwmeta1.element.doi-10_2478_v10037-007-0021-8,
     author = {Yuzhong Ding and Zhiyong Pang},
     title = {Congruences and Quotient Algebras of BCI-algebras},
     journal = {Formalized Mathematics},
     volume = {15},
     year = {2007},
     pages = {175-180},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-007-0021-8}
}

Yuzhong Ding; Zhiyong Pang. Congruences and Quotient Algebras of BCI-algebras. Formalized Mathematics, Tome 15 (2007) pp. 175-180. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-007-0021-8/

[1] Grzegorz Bancerek. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.

[2] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.

[3] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.

[4] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.

[5] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.

[6] Yuzhong Ding. Several classes of BCI-algebras and their properties. Formalized Mathematics, 15(1):1-9, 2007.

[7] Yisheng Huang. BCI-algebras. Science Press, 2006.

[8] Library Committee of the Association of Mizar Users. Binary operations on numbers. To appear in Formalized Mathematics.

[9] Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990.

[10] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.

[11] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.

[12] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

[13] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.

[14] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

[15] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Formalized Mathematics, 1(1):85-89, 1990.