Title | On the algebraic properties of convex bodies and related algebraic systems |
Publication Type | Journal Article |
Year of Publication | 1999 |
Authors | Markov S |
Journal | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
Volume | 91 |
Issue | Livre 1 - Mathématiques et Mecanique |
Pagination | 41-59 |
ISSN | 0205-0808 |
Keywords | convex bodies, quasilinear systems |
Abstract | 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. |
1991/95 MSC | main 52A01, secondary 13C99 |
Attachment | Size |
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91-041-059.pdf | 1.81 MB |