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Length theorems for the general linear group of a module over a local ring

  • Erich W. Ellers (a1) and Huberta Lausch (a2)
Abstract

Let R be a not necessarily commutative local ring, M a free R-module, and π ∈ GL(M) such that B(π) = im(π –1)is a subspace of M. Then π = σ1…σtρ, where σi are simple mappings of given types, ρ is a simple mapping, B(sgr;i) and B(ρ) are subspaces and t ≤ dim B(π).

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Copyright
COPYRIGHT: © Australian Mathematical Society 1989
References
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[1]Cohn, P. M., Free rings and their relations (Academic Press, London, New York, 1971).
[2]Ellers, E. W., ‘Decomposition of equiaffinities into reflections’, Geom. Dedicata 6 (1977), 297–304.
[3]Ellers, E. W., ‘Decomposition of orthogonal, symplectic, and unitary isometries into simple isometries’, Abh. Math. Sem. Univ. Hamburg 46 (1977), 97–127.
[4]Ellers, E. W., ‘Products of axial affinities and products of central collineations’, The geometric vein, Coxeter-Festschrift (pp. 465–470) Springer-Verlag, New York, Heidelberg, Berlin, 1982.
[5]Ellers, E. W. and Frank, R., ‘Products of quasi-reflections and transvections over local rings’, J. Geom. 31 (1988), 69–78.
[6]Ellers, E. W. and Iashibashi, H., ‘Factorization of transformations over a local ring’, Linear Algebra Appl. 85 (1987), 17–27.
[7]Ellers, E. W. and Lausch, Huberta, ‘Generators for classical groups of modules over local rings’ (preprint).
[8]Klingenberg, W., ‘Projektive Geometrie und lineare Algebra über verallgemeinerten Bewetungsrlngen’, Algebraical and topological foundations of geometry, Proc. Colloq. Utrecht, 1959, pp. 99–107 (Pergamon, Oxford, 1962).
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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