Abstract:

We recall the definition of the Grothendieck group of an exact category and  describe the Grothendieck groups of schemes and rings. We define the first  K-theory group of a ring via a short exact sequence of groups and prove  Whitehead's lemma. If time permits, we define K_0 and K_1-regularity of a ring and prove that a regular ring is K_0 and K_1-regular.

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