**ERHARD AICHINGER**

*
On maximal ideals of tame near-rings
*

**Pages** 215-233

**Received:** 10 October 1999

**Mathematics Subject Classification (2000):** 16Y30

**Abstract**
Let N be a zero-symmetric near-ring with identity, and
let G
be a faithful tame N-group.
We prove that every maximal ideal of N is either
dense in N or equal to the annihilator of a section in the
submodule lattice of G.
We study the case that there is precisely one maximal ideal:
often this maximal ideal has to be 0.
As a consequence, we see that if the near-ring
of zero-preserving polynomial functions on a finite
W-group V
has precisely one maximal ideal, then V is either simple or
nilpotent.
Finally, we look at groups G for which the near-rings
I(G), A(G), and E(G) have precisely one maximal ideal, or
are even simple.

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