On Near-Rings With Matrix Units

A radical for right near‐rings: The right Jacobson radical oftype‐0

“…We recall some of the definitions and results of [3] which are required to observe that right Jacobson radicals are relevant for the study of near-rings in terms of matrix nearrings.…”

“…Let G be a finite simple nonabelian additive group. By [3,Corollary 19], E(G 2 ) is isomorphic to the matrix near-ring M 2 (E(G)). As mentioned soon after [ The mapping e 12 : G 2 → G 2 defined by e 12 ((a 1 ,a 2 )) = (a 2 ,0) is an endomorphism of G 2 .…”

“…The structure of matrix near-rings was studied by Rao in [3,4]. It is clear from these papers that right Jacobson-type radicals have an important role to play in the study of Meldrum-van der Walt matrix near-rings.…”

Kurosh–Amitsur Right Jacobson Radicals of Type-1 and 2 for Right Near-Rings

“…In [4] and [5] the first author studied the structure of near-rings in terms of right ideals and shown that as in rings, matrix units determined by right ideals identifies matrix near-rings. In order to show the importance of the right Jacobson radicals of near-rings in the extension of a form of the Wedderburn-Artin theorem of rings involving matrix rings to near-rings, the right Jacobson radicals of type-ν were introduced and studied by the first and second authors in [6][7][8] and [9], ν ∈ {0, 1, 2, s}.…”