Generalized Hamel basis and basis extension in convex cones and uniquely divisible semigroups

I. V. Orlov

Department of Mathematics and Informatics, Crimean Federal V. Vernadsky University, 4 Academician Vernadsky Ave., 295007 Simferopol, Republic Crimea, Russia

Abstract: In the work, a concept of sublinear independence in an arbitrary convex cone is introduced and the corresponding generalization of Hamel basis is studied. Applying these results to the cones generated by uniquely divisible semigroups ((UD)-semigroups) allows us to extend obtained results for the class of (UD)-semigroups. Some applications are considered.

Keywords and phrases: Hamel basis, convex cone, sublinear independence, divisible semigroup, uniquely divisible semigroup, cancellation law.

MSC: 20M14, 47L07, 49J52

Received: 23.08.2016
Revised: 16.04.2017

Language: English