In this chapter, we consider sets with at least two internal operations, which are connected by different distributive laws. Fields and rings are the most common representatives of this kind. It turns out that even those structures that initially appear rather artificial, have well-known and common models, or are useful in applications. Finally, we give a brief insight into the so-called Universal Algebra.

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From Semirings to Fields

  • Kolja Knauer,
  • Ulrich Knauer

摘要

In this chapter, we consider sets with at least two internal operations, which are connected by different distributive laws. Fields and rings are the most common representatives of this kind. It turns out that even those structures that initially appear rather artificial, have well-known and common models, or are useful in applications. Finally, we give a brief insight into the so-called Universal Algebra.