How do I locate a particular theorem in Linear Algebra that I need for my research?
I have been to conferences which seriously discussed a unified and universal bank of all known math theorems. Theoretically, all proven math theorems could be connected logically: A implies B. But, in reality, most proven math theorems are scattered throughout the literature.
I have no access to a university with math journals.
I might be able to do inter-library loan at my local community county college here in the United States. But, that may take a long time. I have no paid job. My earned income is only from social security disability.
Specifically, I need to know:
Let R be a commutative ring. Let M be a square matrix with entries in R. Suppose det(M) factors over R, i.e. is reducible over R, i.e. there exist A and B in R such that A and B are not units in R and det(M)=A*B. Prove there exist square matrices
U and V with entries in R such that detU=A and detV=B.
I believe I can prove this for myself. However, I had to reinvent the wheel.