
Modules are best initially thought of as abelian groups with additional structure. In particular, we would expect most of the basic facts we derived earlier for groups (hence for abelian groups) …
sub-modules. Proposition 2. Given a sub-R-module S ⊂ M, the quotient abelian group: M/S = {m + S | m ∈ M}/ ∼ is an R-module wit product a(m + S) = am + S.
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.
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 …
Modules are a generalization of the vector spaces of linear algebra in which the \scalars" are allowed to be from an arbitrary ring, rather than a ̄eld. This rather modest weakening of the …
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 .