Soft Quasi-ideals of soft near-rings
1Post Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College, Periyar University, Rasipuram, Namakkal District, Tamilnadu, 637401, India
2Post Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College, Periyar University, Rasipuram, Namakkal District, Tamilnadu, 637401, India; Post Graduate and Research Department of Mathematics, Government Arts College, Periyar University, Salem, 636007, Tamilnadu, India
3Department of Mathematics and Science Education, Faculty of Education, Amasya University, 05100, Amasya, Türkiye
2Post Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College, Periyar University, Rasipuram, Namakkal District, Tamilnadu, 637401, India; Post Graduate and Research Department of Mathematics, Government Arts College, Periyar University, Salem, 636007, Tamilnadu, India
3Department of Mathematics and Science Education, Faculty of Education, Amasya University, 05100, Amasya, Türkiye
Sigma J Eng Nat Sci 2023; 41(3): 565-574 DOI: 10.14744/sigma.2023.00062
Abstract
In this paper, we introduce the notions of soft quasi-ideal, soft minimal quasi-ideal, soft left (resp. right) N- subgroup and soft invariant subnear-ring of a soft near-ring with the help of soft set theory established by Molodtsov. We also introduce the concepts of soft zero-sym-metric near-ring, soft constant near- ring, soft near-field and soft Q- simple near-ring over a near-ring. We investigate the properties of these notions with illustrative examples. We obtain the characterizations of soft quasi-ideals of a soft (zero-symmetric) near-ring and soft near-fields over a near-ring.
Keywords: Soft Near-Ring; Soft Quasi-İdeal; Soft Zero-Symmetric Near-Ring; Soft Constant Near-Ring; Soft Q-Simple Near-Ring; Soft Near-Field; Soft Minimal Quasi-İdeal
