BCI-algebras with Condition (S) and their Properties
Tao Sun ; Junjie Zhao ; Xiquan Liang
Formalized Mathematics, Tome 16 (2008), p. 65-71 / Harvested from The Polish Digital Mathematics Library

In this article we will first investigate the elementary properties of BCI-algebras with condition (S), see [8]. And then we will discuss the three classes of algebras: commutative, positive-implicative and implicative BCK-algebras with condition (S).MML identifier: BCIALG 4, version: 7.8.09 4.97.1001

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:267500
@article{bwmeta1.element.doi-10_2478_v10037-008-0010-6,
     author = {Tao Sun and Junjie Zhao and Xiquan Liang},
     title = {BCI-algebras with Condition (S) and their Properties},
     journal = {Formalized Mathematics},
     volume = {16},
     year = {2008},
     pages = {65-71},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0010-6}
}
Tao Sun; Junjie Zhao; Xiquan Liang. BCI-algebras with Condition (S) and their Properties. Formalized Mathematics, Tome 16 (2008) pp. 65-71. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0010-6/

[1] Grzegorz Bancerek. Curried and uncurried functions. Formalized Mathematics, 1(3):537-541, 1990.

[2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.

[3] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.

[4] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 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] Yuzhong Ding and Zhiyong Pang. Congruences and quotient algebras of BCI-algebras. Formalized Mathematics, 15(4):175-180, 2007.

[8] Jie Meng and YoungLin Liu. An Introduction to BCI-algebras. Shaanxi Scientific and Technological Press, 2001.

[9] Andrzej Trybulec. Semilattice operations on finite subsets. Formalized Mathematics, 1(2):369-376, 1990.

[10] Wojciech A. Trybulec. Binary operations on finite sequences. Formalized Mathematics, 1(5):979-981, 1990.

[11] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.

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