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Keywords = neutrosophic quadruple rings

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15 pages, 806 KB  
Article
The Structure of Idempotents in Neutrosophic Rings and Neutrosophic Quadruple Rings
by Yingcang Ma, Xiaohong Zhang, Florentin Smarandache and Juanjuan Zhang
Symmetry 2019, 11(10), 1254; https://doi.org/10.3390/sym11101254 - 8 Oct 2019
Cited by 15 | Viewed by 2679
Abstract
This paper aims to reveal the structure of idempotents in neutrosophic rings and neutrosophic quadruple rings. First, all idempotents in neutrosophic rings R I are given when R is C , R , Q , Z or Z n . [...] Read more.
This paper aims to reveal the structure of idempotents in neutrosophic rings and neutrosophic quadruple rings. First, all idempotents in neutrosophic rings R I are given when R is C , R , Q , Z or Z n . Secondly, the neutrosophic quadruple ring R T I F is introduced and all idempotents in neutrosophic quadruple rings C T I F , R T I F , Q T I F , Z T I F and Z n T I F are also given. Furthermore, the algorithms for solving the idempotents in Z n I and Z n T I F for each nonnegative integer n are provided. Lastly, as a general result, if all idempotents in any ring R are known, then the structure of idempotents in neutrosophic ring R I and neutrosophic quadruple ring R T I F can be determined. Full article
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