A Talk on Commutative Algebra
             Forcing Linearity Numbers

Abstract: Beyond the class of homomorphisms, there are other interesting 
classes of functions between modules.  For example, consider the homogeneous 
functions M(R,V)={f:V->V such that f(rv)=rf(v) for every r in R and for 
every v in V} where R is a commutative ring with identity and V is an 
R-module.  The functions in M(R,V) may or may not be linear in the sense 
that f(v+w) may not be equal to f(v)+f(w).  Certain mathematicians have 
found a rich field of study in investigating how linear a class of functions 
is.  One measure of their linearity is called the forcing linearity number.  
This talk will discuss exactly what this number is and how it is determined 
for some special classes of modules using the theory of commutative 
Noetherian rings and Dedekind domains.