# K-theory of category of finitely presented modules

- Written by O. Sorokin
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*Department of Discrete Analysis and Intelligent SystemFaculty of Applied Mathematics and Informatics Ivan Franko National University of Lviv*

**Abstract:**

We will present a short description of higher K-theory fundamental notions. Higher K-groups Kn will be defined using the Volodin’s acyclic space method for “+”-construction. Moreover, it will be given the brief overview why the stable range notion stabilizes the “infinite” constructions and makes them “finite”. Finally, the explicit description of weak K-space K’(R) will be determined via Gillet-Grayson theorem and double short exact sequences calculus.

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