September 1, 2018 at 7:00 pm

Ring Theory Seminar | Projective and Simple Bases of Infinite Dimensional Algebras, Sept. 21

Rebin Muhammad, portrait

Rebin Muhammad

The Ohio University-Ohio State University ring theory seminar series presents Rebin Muhammad discussing “Projective and Simple Bases of Infinite Dimensional Algebras” on Friday, Sept. 21, at 4:45 p.m. in Cockins Hall 240, OSU-Columbus.

Muhammad is a graduate student in Mathematics at Ohio University.

Abstract: A basis B over an infinite dimensional F-algebra A is called amenable if F^B , the direct product indexed by of copies of the field F, can be made into an A-module in a natural way. When this happens we say that F^B is a basic module. (Mutual) congeniality is a relation that serves to identify cases when different amenable bases yield isomorphic basic A-modules. If B is congenial to C but C is not congenial to B, then we say that B is properly congenial to C. An amenable basis B is called simple if it is not properly congenial to any other amenable basis and it is called projective if there does not exist any amenable basis which is properly congenial to B.
We introduce a family of algebras, which we call graph magma algebras, to study these notions in that context. In particular, we show that the family includes examples of algebras without simple or projective bases. If time allows it, we will explore amenability related questions for a new type of algebra, which we introduce here that we call two-value algebras.

This talk is a report on ongoing joint work with Pınar Aydoğdu and Sergio R. Lopez-Permouth.

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