### Algebraic K-theory of monoid rings, by Joseph Gubeladze

The progress made during last years in the direction mentioned in the title is
described. More precisely, `classical' theorems concerning stable and
non-stable homotopic behavior of algebraic K-functors (starting point of which
are Grothendieck-Serre's theorem on K_0-regularity of a regular ring and
Quillen-Suslin's solution of Serre's problem) were generalized (including higher
K-functors) to the monoid ring extensions corresponding to commutative
cancellative monoids. In many cases these generalizations are stated in a final
(i.e. maximal possible) form. However, recent minor results for higher
K-functors show limitations in general of the posibility for such
generalizations. Relevant ring theoretic topics are also treated.

Joseph Gubeladze <gubel@imath.kheta.ge>