| Summary: | In complex rings or complex fields, the notion of imaginary element <i>i</i> with <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>i</mi> <mn>2</mn> </msup> <mo>=</mo> <mo>−</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula> or the complex number <i>i</i> is included, while, in the neutrosophic rings, the indeterminate element <i>I</i> where <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>I</mi> <mn>2</mn> </msup> <mo>=</mo> <mi>I</mi> </mrow> </semantics> </math> </inline-formula> is included. The neutrosophic ring <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">〈</mo> <mi>R</mi> <mo>∪</mo> <mi>I</mi> <mo stretchy="false">〉</mo> </mrow> </semantics> </math> </inline-formula> is also a ring generated by <i>R</i> and <i>I</i> under the operations of <i>R</i>. In this paper we obtain a characterization theorem for a semi-idempotent to be in <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">〈</mo> <msub> <mi>Z</mi> <mi>p</mi> </msub> <mo>∪</mo> <mi>I</mi> <mo stretchy="false">〉</mo> </mrow> </semantics> </math> </inline-formula>, the neutrosophic ring of modulo integers, where <i>p</i> 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.
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