Tensor Products
Let R be a commutative ring with 1. By keeping track of left and right modules, this
can also be done for noncommutative rings. Let M, N, B be R-modules.
Definition. A function f : M N
Modules over a PID: Applications to matrices
We assume all the usual facts about polynomial rings over a field as well as basic linear
algebra. From this we develop the Jordan and rational canonical f
Topics in commutative ring theory
From now on all rings are commutative with 1.
Definition. The nilradical of a ring R, denoted Nil R, is the set of all nilpotent elements
in R.
Notice that Nil R is a
Bilinear and Quadratic Forms
In this chapter, F will always denote a field of characteristic different from 2 and F will
denote the multiplicative group of nonzero elements.
Definition. An n-ary (or r
Semisimple Rings and Modules
For this section, R will denote any ring with 1.
Definition. The Jacobson radical of R, denoted Rad R, is the intersection of all maximal
left ideals of R.
Examples: Rad Z
Lattices and Boolean algebras
This includes topics of combinatorial interest, with applications in many areas including
computer science and logic. The areas are well represented in the UH Math Depart