Ring Theory Seminar | Row and Column Finite Matrices, Dec. 4

The Ohio University-Ohio State University Ring Theory Seminar holds its last meeting of the fall semester on Friday, Dec. 4, at 4:45 p.m. in Columbus.

Dan Bossaller, Ohio University, presents on “Row and Column Finite Matrices.”

Abstract: In most treatments of linear algebra, one only considers the case when a given $k$-vector space $V$ is finite-dimensional. Indeed, the ring of endomophisms of the free $R$-module $M_R$ over a finite basis $\{e_i | 1 \leq i \leq n\} is isomorphic to the matrix ring $M_n(R)$. In the case of a countably infinite basis $B$, the ring of endomorphisms is isomorphic to the ring $CFM(R)$ of column finite matrices. In this talk, I will present a proof from a 2007 paper by Pace Neilsen that for every column finite matrix $A$with entries from the ring $R$ there exists a matrix $U$ such that $U^{-1}AU$ is both row and column finite if and only if the ring $R$ is noetherian.