Commutative Algebra
A module is a mathematical structure that generalizes the concept of vector spaces by allowing scalars to come from a ring instead of a field. In this way, modules can be viewed as a collection of objects that can be added together and multiplied by elements from a ring, forming a rich algebraic framework. Modules are connected to various concepts, including ring homomorphisms which preserve the module structure and tensor products that help to combine and manipulate modules in more complex ways.
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