SOME NEW NEAR-RINGS FROM OLD RINGS

In this paper, from the given ring (R, +, .), we will construct that a new kind of near-rings, that is, (e, t)-near-ring (R, +, *) with given addition in R and new multiplication * which is expressed in terms of the original multiplication and addition by defining a * b to be a polynomial in a and b, where e and t are fixed (central) orthogonal idempotents in R. Next, we will give some examples and study related substructures of (e, t)-near-rings and those of base rings.