Forcing linearity numbers of certain types of infinitely generated modules over commutative rings.

摘要

Beyond the class of homomorphisms, there are other interesting classes of functions between modules. For example, consider the homogeneous functions M_R(V) = {lcub}f : V → V such that f(rv) = rf(v) for every r ∈ R and for every v ∈ V{rcub} 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 field of study in investigating how linear a class of functions is. One measure of their linearity is called the forcing linearity number.; In this dissertation we determined the forcing linearity numbers for injective modules over Dedekind domains, semisimple modules over integral domains, and semicyclic modules over commutative Noetherian rings.