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Left ideals in the near-ring of affine transformations

Published online by Cambridge University Press:  17 April 2009

Wolfgang Mutter
Wolfgang Mutter
Affiliation:
Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstr. 1 ½, D-8520 Erlangen, Federal Republic of Germany
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Abstract

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In this paper we determine the left ideals in the near-ring Aff(V) of all affine transformations of a vector space V. It is shown that there is a Galois correspondence between the filters of affine subspaces of V and those left ideals of Aff(V) which are not left invariant. In particular, the not left invariant finitely generated left ideals of Aff(V) are precisely the annihilators of the affine subspaces of V. A similar correspondence exists between the filters of linear subspaces of V and the left invariant left ideals of Aff (V). If V is finite-dimensional, then all left ideals of Aff(V) are finitely generated.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 1 , February 1991 , pp. 115 - 122
Copyright
Copyright © Australian Mathematical Society 1991

References

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