INTRODUCTION TO AN ALGEBRAIC THEORY OF ARROWS, III

Abstract

This article is the third part of P. series of investigations on an algebraic theory of arrows or sliding vectors, the first two parts [1, 2] of which are published in this Annual. It is dedicated mainly to the finite systems of arrows In complex standard vector spaces or, more generally, in standard vector spaces over the complex extensions of arbitrary ordered fields. The definitions of these spaces, as well as some basic moments of their algebras, are given in the introductory part of the article [2]; for a more detailed exposition in this connection the reader is referred to the paper [3] or to the booklet [4]. It is remarkable that no essential divergences are observed between the real and the complex cases of arrow algebra. The rank-theorem plays the same central role in the theory of complex arrows as in that of the real ones.