[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2010.25.3.365

ON MEDIAL Q-ALGEBRAS

Ahn, Sun-Shin (DEPARTMENT OF MATHEMATICS EDUCATION DONGGUK UNIVERSITY)
So, Keum-Sook (DEPARTMENT OF MATHEMATICS HALLYM UNIVERSITY)

Publication Information

Communications of the Korean Mathematical Society / v.25, no.3, 2010 , pp. 365-372 More about this Journal

Abstract

In this paper, we show that the mapping ${\varphi}(x)\;=\;0*x$ is an endomorphism of a Q-algebra X, which induces a congruence relation "~" such that X/ $\varphi$ is a medial Q-algebra. We also study some decompositions of ideals in Q-algebras and obtain equivalent conditions for closed ideals. Moreover, we show that if I is an ideal of a Q-algebra X, then $I^g$ is an ignorable ideal of X.

Keywords

Q-algebra; medial Q-algebra;

Citations & Related Records

Times Cited By SCOPUS : 0

Reference

1	S. S. Ahn and H. S. Kim, On QS-algebras, J. Chungcheong Math. Soc. 12 (1999), 33–41.
2	Q. P. Hu and X. Li, On BCH-algebras, Math. Sem. Notes Kobe Univ. 11 (1983), no. 2, part 2, 313–320.
3	Q. P. Hu and X. Li, On proper BCH-algebras, Math. Japon. 30 (1985), no. 4, 659–661.
4	K. Iseki, On BCI-algebras, Math. Sem. Notes Kobe Univ. 8 (1980), no. 1, 125–130.
5	K. Iseki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Japon. 23 (1978/79), no. 1, 1–26.
6	Y. B. Jun, E. H. Roh, and H. S. Kim, On BH-algebras, Sci. Math. 1 (1998), no. 3, 347–354
7	J. Neggers, S. S. Ahn, and H. S. Kim, On Q-algebras, Int. J. Math. Math. Sci. 27 (2001), no. 12, 749–757. DOI ScienceOn
8	J. Neggers and H. S. Kim, On d-algebras, Math. Slovaca 49 (1999), no. 1, 19–26.