#### Thesis Title

Application of the Tor Functor on Commutative R-Modules

#### Date of Graduation

Summer 1998

#### Degree

Master of Science in Mathematics

#### Department

Mathematics

#### Committee Chair

Cameron Wickham

#### Subject Categories

Mathematics

#### Abstract

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.

#### Copyright

© Grant Lathrom

#### Recommended Citation

Lathrom, Grant, "Application of the Tor Functor on Commutative R-Modules" (1998). *MSU Graduate Theses*. 855.

https://bearworks.missouristate.edu/theses/855

**Dissertation/Thesis**