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
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Mathematics and Mathematical Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
