Monthly Archives: June 2013

Elementary Module Theory (II)

Posted on June 29, 2013 by limsup

Having defined submodules, let’s proceed to quotient modules. Unlike the case of groups and rings, any submodule can give a quotient module without any additional condition imposed. Definition. Let N be a submodule of M. By definition, it’s an additive … Continue reading →

Posted in Notes | Tagged , , , , , , , | Leave a comment

Elementary Module Theory (I)

Posted on June 20, 2013 by limsup

Modules can be likened to “vector spaces for rings”. To be specific, we shall see later that a vector space is precisely a module over a field (or in some cases, a division ring). This set of notes assumes the … Continue reading →

Posted in Notes | Tagged , , , , , , , | Leave a comment

Quick Guide to Character Theory (III): Examples and Further Topics

Posted on June 3, 2013 by limsup

G10(a). Character Table of S4 Let’s construct the character table for . First, we have the trivial and alternating representations (see examples 1 and 2 in G1), both of which are clearly irreducible. Next, the action of G on {1, 2, 3, … Continue reading →

Posted in Notes | Tagged , , , , , , | Leave a comment