JP Journal of Algebra, Number Theory and Applications
Volume 39, Issue 4, Pages 479 - 505
(August 2017) http://dx.doi.org/10.17654/NT039040479 |
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ON 2-ABSORBING FUZZY IDEALS
Rabah Kellil
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Abstract: The origin of the present study is the paper [1], where the author studied the concept of 2-absorbing ideals in commutative rings. Many classical theorems on ideals have been used to arrive at the results.In our paper to define the equivalent in the case of fuzzy concepts, we establish the equivalent of the cited theorems as Theorem 2.1 in [2] and Theorem 1 in [4]. In order to establish these equivalent versions, we introduce the notion of the sum of fuzzy ideals, ideals generated by an element, different from those introduced in previous studies as in [5] and [6].
We think that the results presented in this study can be viewed as a generalization of those obtained in the case of crisp theory obtained, in particular, in [1]. However, we investigate the results in [3], and then give a global theory. |
Keywords and phrases: fuzzy sets, fuzzy ideal, radical, strong radical, 2-absorbing ideal, prime ideal, sum of ideals. |
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