Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
8
7
14
8888
13
en
jalali
1392
2
1
gregorian
2013
5
1
8
1
online
1
fulltext
en
Radical and It’s Applications in BCH-Algebras
عمومى
General
پژوهشي
Research paper
<p>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.</p>
Ideal, radical, Quotient $BCH$-algebra, Maximal, Translation.
15
29
http://ijmsi.ir/browse.php?a_code=A-10-1-122&slc_lang=en&sid=1
R.A.
Borzooei
`10031947532846002222`

10031947532846002222
Yes
O.
Zahiri
`10031947532846002223`

10031947532846002223
No