AU - Borzooei, R.A. AU - Zahiri, O. TI - Radical and It’s Applications in BCH-Algebras PT - JOURNAL ARTICLE TA - IJMSI JN - IJMSI VO - 8 VI - 1 IP - 1 4099 - http://ijmsi.ir/article-1-399-en.html 4100 - http://ijmsi.ir/article-1-399-en.pdf SO - IJMSI 1 AB  - 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. CP - IRAN IN - LG - eng PB - IJMSI PG - 15 PT - Research paper YR - 2013