Processing Ion Beam Mixed Nickel/Polyimide Thin Films
Date of Graduation
Master of Science in Materials Science
Physics, Astronomy, and Materials Science
Materials Science and Engineering
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.
© Lisa K Elder
Elder, Lisa K., "Processing Ion Beam Mixed Nickel/Polyimide Thin Films" (1998). MSU Graduate Theses. 846.