Homomorphism and isomorphism theorems generalized from a relational perspective

  • Authors:

  • Gunther Schmidt

  • Affiliations:

  • Institute for Software Technology, Department of Computing Science, Universität der Bundeswehr München, Neubiberg, Germany

  • Venue:
  • RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
  • Year:
  • 2006

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Abstract

The homomorphism and isomorphism theorems traditionally taught to students in a group theory or linear algebra lecture are by no means theorems of group theory. They are for a long time seen as general concepts of universal algebra. This article goes even further and identifies them as relational properties which to study does not even require the concept of an algebra. In addition it is shown how the homomorphism and isomorphism theorems generalize to not necessarily algebraic and thus relational structures.