In the first chapters of this book we set up axioms and calculation rules. We used them for elements of sets, mostly numbers, with concretely given operations. In Chaps. 7 – 10 we have formulated these axioms and calculation rules for elements of general algebraic structures. We applied them to elements of semigroups, rings and fields or acts, modules and vector spaces. For graphs or ordered sets the situation is different. These sets are not structured by operations of the elements, but by more general relations, namely edges or order relations. Nevertheless, results such as the Homomorphism Theorem also apply to graphs or even ordered sets.

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  • Kolja Knauer,
  • Ulrich Knauer

摘要

In the first chapters of this book we set up axioms and calculation rules. We used them for elements of sets, mostly numbers, with concretely given operations. In Chaps. 7 – 10 we have formulated these axioms and calculation rules for elements of general algebraic structures. We applied them to elements of semigroups, rings and fields or acts, modules and vector spaces. For graphs or ordered sets the situation is different. These sets are not structured by operations of the elements, but by more general relations, namely edges or order relations. Nevertheless, results such as the Homomorphism Theorem also apply to graphs or even ordered sets.