University of Guilan Journal of Algebra and Related Topics 2345-3931 9 2 2021 12 01 Valuation near rings 95 100 5301 10.22124/jart.2021.19101.1261 EN E. Khodadadpour Department of Mathematics, Kerman Branch, Islamic Azad University Kerman, Iran T. Roodbarylor Department of Mathematics, Kerman Branch, Islamic Azad University Kerman, Iran Journal Article 2021 03 07 In this paper, the authors have defined the valuation near ring. They have proved some<br />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,<br />the symbol valuation $N$-group in near rings has been introduced. Finally, every valuation $N$-group<br />is a valuation near ring. quotient near ring valuation near ring valuationN-group https://jart.guilan.ac.ir/article_5301_c1b24decc85d3c77cfc31b0105f4c715.pdf