What is "algebras"

Usage examples of "algebras".

It meant foregoing sea cliffs for seminar rooms, but in the rainy seasons he had done it, sitting in on the group’s afternoon meetings, listening to the presentations and the discussions afterward, studying the scrawled math on the screens and spending his mornings working on Riemann surfaces, Lie algebras, Euler numbers, the topologies of compact six-dimensional spaces, differential geometries, Grassmannian variables, Vlad’s emergence operators, and all the rest of the mathematics necessary to follow what the current generation was talking about.

It meant foregoing sea cliffs for seminar rooms, but in the rainy seasons he had done it, sitting in on the group's afternoon meetings, listening to the presentations and the discussions afterward, studying the scrawled math on the screens and spending his mornings working on Riemann surfaces, Lie algebras, Euler numbers, the topologies of compact six-dimensional spaces, differential geometries, Grassmannian variables, Vlad's emergence operators, and all the rest of the mathematics necessary to follow what the current generation was talking about.

Non-commutative algebras (where A times B does not equal B times A) are as self-consistent and meaningful for speakers of Indo-European languages as for speakers of Finno-Ugric.

I achieved only this: I proved that using the apparatus of the topological and transformational algebras would NOT enable one to solve the problem.