Abstract
The aim of this study is to determine the necessary and sufficient condition for any AH subset to be a full ideal in a neutrosophic ring R(I) and to be a nil ideal too. Also, this work shows the equivalence between Kothe’s conjecture in classical rings and corresponding neutrosophic rings, i.e., it proves that Kothe’s conjecture is true in the neutrosophic ring R(I) if and only if it is true in the corresponding classical ring R.
Highlights
It was Zadeh [1] who introduced the notion of fuzzy sets to knob the uncertainties
We determine the conditions of AH subsets to be ideals in the neutrosophic rings with unity
Let R(I) be a neutrosophic ring with unity 1 and M P + SI be any AH subset of R(I); M is a neutrosophic ideal if and only if the following conditions are true: (a) P is an ideal on R
Summary
E aim of this study is to determine the necessary and sufficient condition for any AH subset to be a full ideal in a neutrosophic ring R(I) and to be a nil ideal too. This work shows the equivalence between Kothe’s conjecture in classical rings and corresponding neutrosophic rings, i.e., it proves that Kothe’s conjecture is true in the neutrosophic ring R(I) if and only if it is true in the corresponding classical ring R
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