Semi-Idempotents in Neutrosophic Rings

In complex rings or complex fields, the notion of imaginary element i with i2=-1 or the complex number i is included, while, in the neutrosophic rings, the indeterminate element I where I2=I is included. The neutrosophic ring < RI > 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 < ZpI >, 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.