Characterizing series for faithful d.g. near-rings

Structure Theory of Faithful Rings, Iii. Irreducible Rings

The first two papers of this series1 were primarily concerned with a closure operation on the lattice of right ideals of a ring and the resulting direct-sum representation of the ring in case the closure operation was atomic. These results generalize the classical structure theory of semisimple rings. The present paper studies the irreducible components encountered in the direct-sum representat...

Characterizing Quaternion Rings

We consider the problem of classifying noncommutative R-algebras of low rank over an arbitrary base ring R. We unify and generalize the many definitions of quaternion ring, and give several necessary and sufficient conditions which characterize them. Let R be a commutative, connected Noetherian ring (with 1). Let B be an algebra over R, an associative ring with 1 equipped with an embedding R →֒ ...

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.

Characterizing Reduced Witt Rings Ii

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...