Abstract
In this paper, we introduce the notions of fuzzy semi-maximal ideals and fuzzy primary ideals of an [Formula: see text]-algebra and investigate some of their properties. Also, several characterizations of these fuzzy ideals are given. In addition, we show that [Formula: see text] is a fuzzy semi-maximal ideal of [Formula: see text] if and only if [Formula: see text] is a semi-simple [Formula: see text]-algebra and [Formula: see text] is a fuzzy primary ideal of [Formula: see text] if and only if [Formula: see text] is local [Formula: see text]-algebra. By using the notions of the maximal and normal fuzzy semi-maximal ideals, we show that under certain conditions a fuzzy semi-maximal ideal is two-valued and takes the values 0 and 1. The radical of a fuzzy ideal is defined as against the (maximal) radical of a fuzzy ideal and some of their properties are proved.
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