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Semi-Idempotents in Neutrosophic Rings

Author

Listed:
  • 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)

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.

Suggested Citation

  • Vasantha Kandasamy W.B. & Ilanthenral Kandasamy & Florentin Smarandache, 2019. "Semi-Idempotents in Neutrosophic Rings," Mathematics, MDPI, vol. 7(6), pages 1-7, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:507-:d:236802
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