%0 Journal Article %A Borzooei, R.A. %A Zahiri, O. %T Radical and It’s Applications in BCH-Algebras %J Iranian Journal of Mathematical Sciences and Informatics %V 8 %N 1 %U http://ijmsi.ir/article-1-399-en.html %R 10.7508/ijmsi.2013.01.002 %D 2013 %K Ideal, radical, Quotient $BCH$-algebra, Maximal, Translation., %X Let $X$ be a $BCH$-algebra and $I$ be an ideal of $X$. In this paper, we introduce the concept of $sqrt{I}$. We show that it is an ideal of $X$, when $I$ is closed ideal of $X$. Then we verify some useful properties of it. We prove that it is the ::::union:::: of all $k-$nil ideals of $I$. Moreover, if $I$ is a closed ideal of $X$, then $sqrt{I}$ is a closed translation ideal and so we can construct a quotient $BCH$-algebra. We prove this quotient is a P-semisimple $BCI$-algebra and so it is an abelian group. Then we use the concept of radical in order to construct the second and the third isomorphism theorems. %> http://ijmsi.ir/article-1-399-en.pdf %P 15-29 %& 15 %! %9 Research paper %L A-10-1-122 %+ %G eng %@ 1735-4463 %[ 2013