(untitled) (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 1999)
The algebraic system of convex bodies with addition and multiplication by scalar is studied. A new operation for convex bodies, called inner addition, is introduced. New distributivity relations for xonvex bodies, called resp. quasidistributive and q-distributive law, are formulated and proved. The convex bodies form a quasilinear system with respect to addition and multiplication by scalar. The latter is isomorphically embedded in a q-linear system, which is an abelian group with respect to addition and obeys the q-distributive law. A result of H. Rådström for convex bodies is generalized.