Volume 8, Issue 1 (5-2013)                   IJMSI 2013, 8(1): 15-29 | Back to browse issues page

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Borzooei R, Zahiri O. Radical and It’s Applications in BCH-Algebras. IJMSI. 2013; 8 (1) :15-29
URL: http://ijmsi.ir/article-1-399-en.html

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.

Type of Study: Research paper | Subject: General

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