• FECKLY SEMI REGULAR NEAR-FIELD SPACES OVER NEAR-FIELD

Abstract

Let N be a near-field space and J(N) the Jacobson radical. An element a Î N is called semi regular if there exists a regular element bÎN with a – b Î J(N). A near-field space N is said to be feckly semi regular near-field space provided that any element a Î N, either a or 1 – a is semi regular. I, Dr N V Nagendram as an author introduce, in this paper, feckly semi regular near-field spaces as the generalization of VNL-near-field spaces and semi regular near-field spaces. It is shown that feckly semi regular near-field spaces are exchange near-field spaces and many properties of semi regular near-field spaces can be extended only feckly semi regular near-field spaces. Relative examples are also constructed. All feckly semi regular near-field spaces considered are either near-fields by hypothesis or turn out to be periodic near-field spaces over near-fields in the course of the in depth study and investigation of the near-field spaces over near-fields.