Glossary of Tensor Theory - Abstract Algebra

Abstract Algebra

Tensor product of fields

This is an operation on fields, that does not always produce a field.

Tensor product of R-algebras

Clifford module

A representation of a Clifford algebra which gives a realisation of a Clifford algebra as a matrix algebra.

Tor functors

These are the derived functors of the tensor product, and feature strongly in homological algebra. The name comes from the torsion subgroup in abelian group theory.

Symbolic method of invariant theory

Derived category Grothendieck's six operations

These are highly abstract approaches used in some parts of geometry.