Document Type : Research Paper
Department of Mathematics, Kerman Branch, Islamic Azad University Kerman, Iran
In this paper, the authors have defined the valuation near ring. They have proved some
theorem, for example, they have shown every valuation near ring is a local near ring and the ideals of N are totally ordered by inclusion. Also,
the symbol valuation $N$-group in near rings has been introduced. Finally, every valuation $N$-group
is a valuation near ring.