The J2-radical in structural matrix near-rings

The Baer Radical of Generalized Matrix Rings

In this paper, we introduce a new concept of generalized matrix rings and build up the general theory of radicals for g.m.rings. Meantime, we obtain r̄b(A) = g.m.rb(A) = ∑ {rb(Aij) | i, j ∈ I} = rb(A)

Matrix maps over planar near-rings

Following a method by Meldrum and van der Walt, near-rings of matrix maps are defined for general near-rings, not necessarily with identity. The influence of one-sided identities is discussed. When the base near-ring is integral and planar, the near-ring of matrix maps is shown to be simple. Various types of primitivity of the near-ring of matrix maps are discussed when the base near-ring is pl...

ON ANTI FUZZY IDEALS IN NEAR-RINGS

In this paper, we apply the Biswas’ idea of anti fuzzy subgroups toideals of near-rings. We introduce the notion of anti fuzzy ideals of near-rings,and investigate some related properties.

A radical for right near-rings: The right Jacobson radical of type-0

The notions of a right quasiregular element and right modular right ideal in a near-ring are initiated. Based on these J 0(R), the right Jacobson radical of type-0 of a near-ring R is introduced. It is obtained that J 0 is a radical map andN(R)⊆ J 0(R), whereN(R) is the nil radical of a near-ring R. Some characterizations of J 0(R) are given and its relation with some of the radicals is also di...

Differential Polynomial Rings of Triangular Matrix Rings