Semi-Idempotents in Neutrosophic Rings

Vasantha Kandasamy W.B., Ilanthenral Kandasamy and Florentin Smarandache
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Vasantha Kandasamy W.B.: School of Computer Science and Engineering, VIT, Vellore 632014, India
Ilanthenral Kandasamy: School of Computer Science and Engineering, VIT, Vellore 632014, India
Florentin Smarandache: Department of Mathematics, University of New Mexico, 705 Gurley Avenue, Gallup, NM 87301, USA

Mathematics, 2019, vol. 7, issue 6, 1-7

Abstract: In complex rings or complex fields, the notion of imaginary element i with i 2 = − 1 or the complex number i is included, while, in the neutrosophic rings, the indeterminate element I where I 2 = I is included. The neutrosophic ring 〈 R ∪ I 〉 is also a ring generated by R and I under the operations of R . In this paper we obtain a characterization theorem for a semi-idempotent to be in 〈 Z p ∪ I 〉 , the neutrosophic ring of modulo integers, where p a prime. Here, we discuss only about neutrosophic semi-idempotents in these neutrosophic rings. Several interesting properties about them are also derived and some open problems are suggested.

Keywords: semi-idempotent; neutrosophic rings; modulo neutrosophic rings; neutrosophic semi-idempotent (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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