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Left ideals in the near-ring of affine transformations
Published online by Cambridge University Press: 17 April 2009
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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