  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.
