1-Primitive Near-rings
We give a classification of $1$-primitive near-rings using sandwich centralizer near-rings
math.RA↗
arXiv subjects
Gerhard Wendt
Publications and source records attributed to Gerhard Wendt.
Units in Near-rings
We investigate near-ring properties that generalize nearfield properties about units. We study zero symmetric near-rings $N$ with identity with two interrelated properties: the units with zero form an additive subgroup of $(N,+)$; the units act without fixedpoints on $(N,+)$. There are many similarities between these cases, but also many differences. Rings with these properties are fields, near-rings allow more possibilities, which are investigated. Descriptions of constructions are obtained and used to create examples showing the two properties are independent but related. Properties of the additive group as a $p$-group are determined and it is shown that proper examples are neither simple nor $J_2$-semisimple.
math.RA↗
J2 Radical in Automata Nearrings
Looking at the automata defined over a group alphabet as a nearring, we see that they are a highly complicated structure. As with ring theory, one method to deal with complexity is to look at semisimplicity modulo radical structures. We find some bounds on the Jacobson 2-radical and show that in certain groups, this radical can be explicitly found and the semisimple image determined.
cs.FL↗