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$n$-groups

Proceedings of the Edinburgh Mathematical Society (1)

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ON NEAR-RING IDEMPOTENTS AND POLYNOMIALS ON DIRECT PRODUCTS OF Ω-GROUPS
Erhard Aichinger
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 44 / Issue 2 / June 2001

Published online by Cambridge University Press:

20 January 2009, pp. 379-388
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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