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1
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Several Classes of BCI-algebras and their Properties

100%
Ding Y.
Formalized Mathematics
|
2007
|
tom 15
|
nr 1
1-9
EN
I have formalized the BCI-algebras closely following the book [6], sections 1.1 to 1.3, 1.6, 2.1 to 2.3, and 2.7. In this article the general theory of BCI-algebras and several classes of BCI-algebras are given. MML identifier: BCIALG 1, version: 7.8.04 4.81.962
2
Content available remote

Congruences and Quotient Algebras of BCI-algebras

63%
Ding Y., Pang Z.
Formalized Mathematics
|
2007
|
tom 15
|
nr 4
175-180
EN
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.
3
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Ideals of BCI-algebras and their Properties

63%
Wu C., Ding Y.
Formalized Mathematics
|
2008
|
tom 16
|
nr 2
109-114
EN
In this article three classes of ideals are discussed: associative ideals, commutative ideals, implicative ideals and positive implicative ideals, and their elementary properties. Some of their properties and the relationships between them have not been proven yet, and will be completed in the following article.MML identifier: BCIIDEAL, version: 7.8.10 4.99.1005
4
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BCI-homomorphisms

51%
Ding Y., Ge F., Wu C.
Formalized Mathematics
|
2008
|
tom 16
|
nr 4
371-376
EN
In this article the notion of the power of an element of BCI-algebra and its period in the book [11], sections 1.4 to 1.5 are firstly given. Then the definition of BCI-homomorphism is defined and the fundamental theorem of homomorphism, the first isomorphism theorem and the second isomorphism theorem are proved following the book [9], section 1.6.MML identifier: BCIALG 6, version: 7.9.03 4.108.1028
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