There is also the chapter in P. Halmos, Finite Dimensional Vector Spaces on multi-linear algebra which at the time I read it I took it as an abstract approach to determinants, maybe also a start on exterior algebra of differential forms, but maybe there's a long shot chance that that Halmos chapter is related to multi-dimensional determinants.

Can't read ALL the books on the shelves of the research libraries or even all the recent ones so have to be selective, to focus or as a startup entrepreneur before spending hundreds of hours in such a book (hope the author got tenure) ask "Why should I?".

I am sure Gelfand, Kapranov and Zelevinsky given their other math accomplishments all got tenure track positions when they emigrated. Will give Halmos another look.

That can't still be THE Gel'fand, along with Kolmogorov, prof of E. Dynkin? Must be a great grand son or some such.

He passed recently, but yes it’s that one. The book is from 1994 and the research is from just before USSR fell.