Semi-Idempotents in Neutrosophic Rings

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.

Some Implicativities for Groupoids and BCK-Algebras

“…The notion of Smarandache algebras emerged and has been applied to several algebraic structures [10][11][12]. Two algebras (X, * ) and (X, •) are said to be Smarandache disjoint [13,14] if we add some axioms of an algebra (X, * ) to an algebra (X, •), then the algebra (X, •) becomes a trivial algebra, i.e., |X| = 1; or if we add some axioms of an algebra (X, •) to an algebra (X, * ), then the algebra (X, •) becomes a trivial algebra, i.e., |X| = 1.…”

Characterizations of dual curves and dual focal curves in dual Lorentzian spaceD31

“…Dual numbers were first introduced by William Kingdon Clifford (1873) and by Aleksandr Petrovich Kotelnikov (1895) and it has been employed for some specific applications [4]. Many studies have been conducted in relation to dual numbers and dual Lorentzian space D 3 1 .…”

Neutrosophic Triplets in Neutrosophic Rings

“…Related theories of neutrosophic triplet, duplet, and duplet set were developed by Smarandache [18]. Neutrosophic duplets and triplets have fascinated several researchers who have developed concepts such as neutrosophic triplet normed space, fields, rings and their applications; triplets cosets; quotient groups and their application to mathematical modeling; triplet groups; singleton neutrosophic triplet group and generalization; and so on [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Computational and combinatorial aspects of algebraic structures are analyzed in [37].…”