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?
> 
> 
> 



Looking for a paper on axiomatic orthogonality in a vector space
This journal published by the [Herzen University](https://en.wikipedia.org/wiki/Herzen_University) is not yet available in electronic form.


A paper version can be found in multiple libraries, including the [National Library of Russia](https://webservices.nlr.ru/util/?method=recordFormat&vid=07NLR_VU1&sysid=002516234&format=037&base=NLR01).


They will [scan](http://nlr.ru/shop/pages/edd/edd.php?ss=2d20b9b25f672960b04e17a61ec1f84a) papers for a [nominal fee of about 0.27 USD per page](http://nlr.ru/shop/pages/srv/srv.php?p=5&ss=2d20b9b25f672960b04e17a61ec1f84a).


