Γ- Near- Fields and bi-ideals, Commutativity in Prime Gamma Near-Rings with Permuting Tri-derivations, GENERALIZED PSEUDO COMMUTATIVE GAMMA NEAR-RINGS, PRIME GAMMA-NEAR-RINGS WITH (σ, τ)-DERIVATIONS, Fuzzy Ideals , and many more
A gamma near ring is called a gamma near field provided it has an identity element, at least one nonzero element and every nonzero element has a unique inverse element (see page 37). Gamma near fields are characterized by bi-ideals (see Section 4, starting on page 40).
The commutivity of prime gamma near rings is investigated in
A.M. Ibraheem, On the commutativity of prime gamma near rings, IOSR J of Math. 10 (2), 2014, 68-71:
which references earlier work on semiprime gamma near rings (Y.U. Cho and Y.B. Jun, 2002), prime near rings (Y.U. Cho, 2001 and M. Uckun, M.A. Ozturk, Y.B. Jun, 2004).
This is version VI of the paper. I am assuming that this means that this paper went through VI revisions before it was accepted. Perhaps Afrah Mohammed Ibraheem can comment on this.
The numbering of the references for this paper has mistakes. References
[2] and [3] are the same paper, and
[8] and [9] are the same paper.
The paper
M. Uckun, M.A.Ozturk and Y.B.Jun, On prime gamma-near-rings with derivations, Commun. Korean Math. Soc. 19(3), 2004, 427-433
is a very good paper that includes a thorough overview of previous work on gamma-near rings.
please read the following two papers (first two papers of mine ) (i) "The f-prime radical in -near-rings", South-East Asian Bulletin of Mathematics 23 (1999) 507-511.(Zbl 0947.16033), (ii). "A Note on -near-rings", Indian J. Mathematics (B.N. Prasad Birth Centenary commemoration volume) 41(1999) 427-433.(Zbl 1033.16501)