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Rings and Modules Seminar
~ Abstracts ~

Yang Zhang
zhang39(at)cc(dot)umanitoba(dot)ca

Department of Mathematics
University of Manitoba

Monday, March 22, 2010

Normal Forms of Quaternionic Polynomial Matrices
Abstract:

The family of quaternions and quaternionic polynomial matrices play important roles in quantum physics and control theory. In this talk, we will define and discuss some normal forms of quaternionc polynomial matrices, such as Hermite form and Popov form.

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oherent but not noetherian; on the surface it appears to be a close relative of the rings Rn. Lorna Gregory, a PhD student of Mike Prest in Manchester, has been looking at the injective envelope of Rω/M, where M is the maximal ideal generated by all the indeterminates. It is not just a "complexified" version of its noetherian relatives. I have a description of a large and complicated essential extension Eo of Rω/M, and Lorna has some nice complexity results, showing how far Eo must be from the injective envelope.

REFERENCES:

  1. E. Matlis, Injective Modules over Noetherian Rings, Pacific J. Math (8) 511--528, 1958.
  2. D. G. Northcott, }, Injective Envelopes and Inverse Polynomials, Journal of the LMS, Series 2, (8) 290--296, 1974.
  3. T. G. Kucera, Explicit descriptions of injective envelopes: generalizations of a result of Northcott, Comm. Algebra, 17(11) 2703--2715, 1989.

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This page maintained by tkucera@cc.umanitoba.ca. Page © 2010 Thomas G. Kucera