Erhard Aichinger,
"On maximal ideals of tame near-rings"
, in Rivista di Matematica della Universita di Parma, 1999, ISSN: 0035-6298, Erhard Aichinger, On maximal ideals of tame near-rings, Rivista di Matematica dell'Universita di Parma (6), Vol.2*, 1999, pp. 215-233
Original Titel:
On maximal ideals of tame near-rings
Sprache des Titels:
Englisch
Englische Kurzfassung:
Let $N$ be a zero-symmetric near-ring with identity, and
let $\Gamma$ 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 $\Gamma$.
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 $\Omega$-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.
Journal:
Rivista di Matematica della Universita di Parma
Erscheinungsjahr:
1999
Notiz zum Zitat:
Erhard Aichinger, On maximal ideals of tame near-rings, Rivista di Matematica dell'Universita di Parma (6), Vol.2*, 1999, pp. 215-233
Forschungs-