I am looking for a paper "Linear spaces with disjoint elements and their conversion into vector lattices" by A. I. Veksler.
It was published in 1967 in Research Notes of Leningrad State Pedagogical University.
The paper is in Russian, and is called "Линейные пространства с дизъюнктными элементами и преврщение их в векторные структуры".
The name of the journal volume is Ученые записки Ленинградского государственного педагогического института им. А. И. Герцена. Т. 328 : Вопросы современной математики / редкол.: И. Я. Бакельман, К. А. Бохан, А. Л. Вернер [и др.]. – Ленинград : Изд-во Ленинград. госуд. ин-та, 1967. – 282 с.
Can anybody help me finding this paper? Either original, or a translation into English will do.
The topic of the paper is an axiomatic approach to the notion of orthogonality (or disjointness) in vector spaces, where a binary relation is introduced, which satisfies certain properties, with an eye on the notion of disjointness in vector lattices (but I don't know the details, since I cannot access the paper). Note that orthogonality in vector spaces appears in several contexts:
In the presence of a bilinear form (the usual orthogonality);
In the presence of multiplication (declare $e\bot f$ if $ef=0$);
In the presence of an order (if $E$ is a Vector lattice, then $e\bot f$ if $|e|\wedge |f|=0$);
If the space consists of functions into a vector space (say that $f,g:X\to F$ are disjoint if $f^{-1}(0)\cup g^{-1}(0)=X$).
There is also a lot of research done on the maps preserving disjointness, in various contexts, but i don't know to what extend it is generalizable. Hence, I wonder what is done on this topic from the axiomatic standpoint. So far the aforementioned paper is the only one I came across, and even that is not accessible.
Does anybody know any other literature on this subject?
