If S is a subring of R then any R-module can be considered as an S-module by restricting scalar multiplication to S M. For example, a complex vector space can be considered as a real vector …

The resulting R-module M=N is called the quotient module of M with re-spect to the submodule N. The noether isomorphism theorems, which we have seen previously for groups and rings, then …

Here we cover all the basic material on modules and vector spaces required for embarkation on advanced courses. Concerning the prerequisite algebraic background for this, we mention that …

All in all the approach chosen here leads to a clear refinement of the customary module theory and, for M = R, we obtain well-known results for the entire module category over a ring with unit.

hicago in Winter 1998. The purpose of the lectures is to give an introduction to the theory of modules over the (sheaf of) algebras of algebraic differential operators .

It can be made into a module when M or N have additional structure. Given another ring S, an (R, S)-bimodule N is an abelian group with a left R-module structure and a right S-module …

Students who have limited experience with decimal fractions may be supported by a return to Grade 4’s Module 6 to review decimal place value and symmetry with respect to the ones place.