radical of $cdot$-ideals in $pmv$-algebras
نویسندگان
چکیده
in this paper, we introduce the notion of the radical of a $pmv$-algebra $a$ and we charactrize radical $a$ via elements of $a$. also, we introduce the notion of the radical of a $cdot$-ideal in $pmv$-algebras. several characterizations of this radical is given. we define the notion of a semimaximal $cdot$-ideal in a $pmv$-algebra. finally we show that $a/i$ has no nilpotent elements if and only if $i$ is a semi-maximal $cdot$-ideal of $a$.
منابع مشابه
Radical of $cdot$-ideals in $PMV$-algebras
In this paper, we introduce the notion of the radical of a $PMV$-algebra $A$ and we charactrize radical $A$ via elements of $A$. Also, we introduce the notion of the radical of a $cdot$-ideal in $PMV$-algebras. Several characterizations of this radical is given. We define the notion of a semimaximal $cdot$-ideal in a $PMV$-algebra. Finally we show that $A/I$ has no nilpotent elemen...
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عنوان ژورنال:
bulletin of the iranian mathematical societyجلد ۴۲، شماره ۲، صفحات ۲۳۳-۲۴۶
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