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ON NEAR-RING IDEMPOTENTS AND POLYNOMIALS ON DIRECT PRODUCTS OF Ω-GROUPS

Published online by Cambridge University Press:  20 January 2009

Erhard Aichinger
Erhard Aichinger
Affiliation:
Institut für Algebra, Stochastik und wissensbasierte mathematische Systeme, J. Kepler Univ., Linz, 4040 Linz, Austria (erhard@algebra.uni-linz.ac.at)
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Abstract

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Let $N$ be a zero-symmetric near-ring with identity, and let $\sGa$ be a faithful tame $N$-group. We characterize those ideals of $\sGa$ that are the range of some idempotent element of $N$. Using these idempotents, we show that the polynomials on the direct product of the finite $\sOm$-groups $V_1,V_2,\dots,V_n$ can be studied componentwise if and only if $\prod_{i=1}^nV_i$ has no skew congruences.

AMS 2000 Mathematics subject classification: Primary 16Y30. Secondary 08A40

Keywords

near-rings$\sOm$-groupspolynomials$N$-groups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 2 , June 2001 , pp. 379 - 388
Copyright
Copyright © Edinburgh Mathematical Society 2001