Application of the Tor Functor on Commutative R-Modules
Date of Graduation
Master of Science in Mathematics
R-modules are algebraic objects which may be considered as generalizations of k-vector spaces. An element a∈A is a torsion element of a module A if there is a nonzerodivisor r∈R such that ra=0. For an arbitrary ring R if we take Q to be the localization of R with respect to the set of nonzerodivisors then we can show for any R-module A the module TorR₁(A, Q/R) is isomorphic to t(A), the torsion submodule of A. Furthermore, if A and B are arbitrary R-modules then in the case where R is a domain we have that TorRn(A, B) is torsion for all n≥1.
© Grant Lathrom
Lathrom, Grant, "Application of the Tor Functor on Commutative R-Modules" (1998). MSU Graduate Theses. 855.