Ehsaan Hossain, Department of Pure Mathematics, University of Waterloo
“The maximal right ring of quotients”
Last week, Hongdi introduced us to the endomorphism ring E = End(IR) of an injective module IR: we saw a nice characterization of the Jacobson radical, and that E/J(E) is von Neumann regular. This time we will see that E/J(E) is self-injective. To construct the maximal right ring of quotients, we take IR = E(RR) to be the injective hull of the regular module RR, and then let Q consist of the rational elements of IR. This is an R-module, but we will see that it has a natural ring structure. In the special cases of Ore domains or semiprime right Goldie rings, Q is the Ore ring of fractions constructed last semester.
This is a brand new topic, completely disjoint from Morita theory — so if you’re interested to join us for this EXCITING new chapter, please do!
MC 5403