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The Mathematical Intelligencer

, Volume 12, Issue 4, pp 10–16 | Cite as

Years ago

The one-hundredth anniversary of the death of invariant theory?
  • Karen V. H. Parshall
Department

Keywords

Linear Transformation British School Binary Quadratic Form Group Representation Theory Quartic Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Boole, p. 19. Note here that Boole only tacitly assumed the nonsingularity of his linear transformation, and all of his calculations were explicit. In what follows, I adhere to the historical presentation as much as possible, while still rendering it comprehensible to the modern reader. Thus, I do not use modern formulations and notations when they would trivialize or otherwise distort the nineteenth-century work.Google Scholar
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    Hilbert’s proof of this theorem, which is not unlike that in most standard algebra textbooks, also goes through under the more general hypothesis of a ringR in which every ideal is finitely generated. See, for example, Nathan Jacobson,Basic Algebra II, San Francisco: W. H. Freeman & Co. (1980), 417–418.zbMATHGoogle Scholar
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    Among other things in this 1893 paper, Hilbert proved his famous Nullstellensatz (in section three). (See note [4] above.) This paper is generally credited with ushering in modern algebra, although as this article hopefully makes clear relative to invariant theory, these sorts of statements generally beg for deeper historical inquiry.Google Scholar
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Copyright information

© Springer Science+Business Media, Inc. 1990

Authors and Affiliations

  • Karen V. H. Parshall
    • 1
  1. 1.Departments of Mathematics and HistoryUniversity of VirginiaCharlottesvilleUSA

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