"I liked the algebraic way of looking at things.
I’m additionally fascinated when the algebraic method is applied to infinite objects”.

Irwing Kaplansky

K-theory of category of finitely presented modules


Olexiy Sorokin

Department of Discrete Analysis and Intelligent System
Faculty of Applied Mathematics and Informatics
Ivan Franko National University of Lviv



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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Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv
1 Universytetska Str., 79000 Lviv, Ukraine
Tel: (+380 322) 394 172
E-mail: oromaniv at

Scientific seminar, May, 2016