radical of filters in residuated lattices
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abstract
in this paper, the notion of the radical of a filter in residuated lattices is defined and several characterizations of the radical of a filter are given. we show that if f is a positive implicative filter (or obstinate filter), then rad(f)=f. we proved the extension theorem for radical of filters in residuated lattices. also, we study the radical of filters in linearly ordered residuated lattices.
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Journal title:
journal of algebraic systemجلد ۴، شماره ۲، صفحات ۱۱۱-۱۲۱
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