|
MATHEMATICS COLLOQUIUM
SERIES
Thursday, October 28, 2004
11:00-12:00, UC 307
Maximal left quotient rings and graded
algebras
Gonzalo Aranda
Departamento de Álgebra,
Geometría y Topología
Universidad de Malaga, Spain
In 1956, Utumi introduced the notion of maximal left
quotient ring for every ring without total right zero divisors. This
notion generalizes the construction of a field of fractions of an integral
domain. This maximal ring can be viewed as the ring where all types of
quotient rings live in. We generalize this construction to the case of
graded algebras, we study some of its properties and we obtain deeper
results when we focus specifically on superalgebras. The work in progress
is trying to obtain similar structure results to those of the non-graded
case, i.e.: Gabriel's and Johnson's theorems.
|
