radical of $cdot$-ideals in $pmv$-algebras

Authors

f. forouzesh

faculty of mathematics and computing‎, ‎higher education complex of bam‎, bam‎, ‎iran.

abstract

‎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 $a$.

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Journal title:
bulletin of the iranian mathematical society

جلد ۴۲، شماره ۲، صفحات ۲۳۳-۲۴۶

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