Linear algebra over general rings

Abstract: In linear algebra we meet solution sets to systems of linear equations with coefficients from a field. Later, we see that we can replace the field by a more general ring, for instance a Weyl algebra where we would be looking at solutions of systems of linear partial differential equations. Over general rings, however, such solution sets do not have nice closure properties; for instance they might not be closed under coordinate projections. But, if we accept projected systems of equations and their solution sets as basic objects, then we recover the nice closure properties that one has over fields and, over general rings, find interesting structures sitting within a rich and extensive theory which ramifies into many aspects of representation theory.

Mathematics

Audience: researchers in the topic

UEA pure maths seminar