The isomorphism theorems for modules are the same as for the (abelian) groups (since modules are abelian groups!). To prove them, it suffices to check that the group isomorphisms …

There is a collection of simple notions concerning modules which have entered algebra from algebraic topology. These concepts are important in developing the theory of homology and …

Modules are weak generalizations of ideals, abelian groups and vector spaces. Although modules are not always like vector spaces, we found that free modules possessed vector-like …

It’s easy to check that any intersection of R-modules is again an R-module, so this definition makes sense. And this definition leads to a few more, but most especially, we say that an R …

Vladimir Baranovsky and Sam Evens 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 …

They have many desirable properties and are central to fields such as representation theory and homological algebra. The main theorem of this presentation is the bijective correspondence …

ras and lattices. The algebraic systems at the center of this two-semester course are rings, modules, g. oups, and fields. Vector spaces are special. cases of modules. These kinds of …