#### Thesis Title

Processing Ion Beam Mixed Nickel/Polyimide Thin Films

#### Date of Graduation

Summer 1998

#### Degree

Master of Science in Materials Science

#### Department

Physics, Astronomy and Materials Science

#### Committee Chair

Ryan Giedd

#### Subject Categories

Materials Science and Engineering

#### 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

© Lisa K Elder

#### Recommended Citation

Elder, Lisa K., "Processing Ion Beam Mixed Nickel/Polyimide Thin Films" (1998). *MSU Graduate Theses*. 846.

https://bearworks.missouristate.edu/theses/846

**Dissertation/Thesis**