On the algebraic properties of convex bodies and related algebraic systems (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.