The Algebra Seminar presents Rebin Muhammad discussing “Amenable and Congenial Bases” on Thursday, April 13, from 4:30-5:30 p.m. in Morton 313.
Muhammad is a graduate student in Mathematics at Ohio University.
Abstract: We survey some recent results leading to my ongoing dissertation research. Let A be an infinite dimensional K- algebra, where K is a field and let B be a basis for A. In this talk we explore a property of the basis B that guarantees that K^B (the direct product of copies indexed by B of the field K) can be made into an A-module in a natural way. We call bases satisfying that property “amenable” and the resulting modules “basic modules.” We explore whether all amenable bases yield isomorphic A-modules. Then we consider a relation (named congeniality) that guarantees that two different bases yield isomorphic A-module structures on K^B. We will look at several examples in the familiar setting of the algebra K[x] of polynomials with coefficients in K and will introduce several general interesting questions in that context. In particular, we introduce so-called simple bases and show a discordant family of simple bases over K[x]. (This talk is mostly based on a recently published paper by Lulwah A-Essa, Sergio R. López-Permouth and Najat Muthana.)
Comments