Congruences and Quotient Algebras of BCI-algebras

Yuzhong Ding; Zhiyong Pang

Formalized Mathematics (2007)

  • Volume: 15, Issue: 4, page 175-180
  • ISSN: 1426-2630

Abstract

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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.

How to cite

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Yuzhong Ding, and Zhiyong Pang. "Congruences and Quotient Algebras of BCI-algebras." Formalized Mathematics 15.4 (2007): 175-180. <http://eudml.org/doc/267323>.

@article{YuzhongDing2007,
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.},
author = {Yuzhong Ding, Zhiyong Pang},
journal = {Formalized Mathematics},
language = {eng},
number = {4},
pages = {175-180},
title = {Congruences and Quotient Algebras of BCI-algebras},
url = {http://eudml.org/doc/267323},
volume = {15},
year = {2007},
}

TY - JOUR
AU - Yuzhong Ding
AU - Zhiyong Pang
TI - Congruences and Quotient Algebras of BCI-algebras
JO - Formalized Mathematics
PY - 2007
VL - 15
IS - 4
SP - 175
EP - 180
AB - 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.
LA - eng
UR - http://eudml.org/doc/267323
ER -

References

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  7. [7] Yisheng Huang. BCI-algebras. Science Press, 2006. 
  8. [8] Library Committee of the Association of Mizar Users. Binary operations on numbers. To appear in Formalized Mathematics. 
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  10. [10] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics. 
  11. [11] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990. 
  12. [12] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  13. [13] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 
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  15. [15] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Formalized Mathematics, 1(1):85-89, 1990. 

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