• A NOTE ON TL-IDEALS OF NEAR-FIELD SPACES OVER REGULAR -NEAR-RINGS

Abstract

The aim of this paper is to introduce and study TL-sub near-fields, TL-ideals of near-fields over regular delta near-rings and to obtain their characterizations. We define T-sum, T-difference, T-product of L-sub near-fields of a near-field N over regular delta near-ring of a ring R and obtain their properties. The set of near-fields of TL-ideals of a near-field N over –field regular delta near-ring of a ring R equipped with L-sub near-fields inclusion relation ≤ constitutes a complete lattice with L- sub near-field intersection as its meet is proved. The quotient near-field (N/µ, +T, *) is obtained and proved that it is isomorphic to the quotient near-field (N/Nµ,+T,*). Also we obtain some characterizations of homomorphism of TL-ideals of near-fields over regular delta near-rings.