The Ohio University-Ohio State University Ring Theory Seminar presents Lulwah Al-Essa on Friday, Feb. 27, at 4:45 p.m. in Cockins Hall 240 at Ohio State University’s Department of Mathematics.
Al-Essa, a doctoral student in Mathematics at Ohio University, will discuss “Modules over Infinite Dimensional Algebras.”
Abstract: 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 we show that not all amenable bases yield isomorphic A-modules. Then we consider a relation (which we name 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. Finally, we will discuss some results regarding these notions in the context of Leavitt Path Algebras (joint work with Sergio R. Lopez-Permouth and Najat Muthana).
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