Special radicals and matrix near-rings

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...

Differential Polynomial Rings of Triangular Matrix Rings

0-primitive Near-rings, Minimal Ideals and Simple Near-rings

We study the structure of 0-primitive near-rings and are able to answer an open question in the theory of minimal ideals in near-rings to the negative, namely if the heart of a zero symmetric subdirectly irreducible near-ring is subdirectly irreducible again. Also, we will be able to classify when a simple near-ring with an identity and containing a minimal left ideal is a Jacobson radical near...

Hereditary right Jacobson radicals of type-1(e) and 2(e) for right near-rings

Near-rings considered are right near-rings. In this paper two more radicals, the right Jacobson radicals of type-1(e) and 2(e), are introduced for near-rings. It is shown that they are Kurosh-Amitsur radicals (KAradicals) in the class of all near-rings and are ideal-hereditary radicals in the class of all zero-symmetric near-rings. Different kinds of examples are also presented.

Unitary Strongly Prime Rings and Related Radicals

A unitary strongly prime ring is defined as a prime ring whose central closure is simple with identity element. The class of unitary strongly prime rings is a special class of rings and the corresponding radical is called the unitary strongly prime radical. In this paper we prove some results on unitary strongly prime rings. The results are applied to study the unitary strongly prime radical of...