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Theory of Modules: Course Contents (MAT 458)

A module over a ring is a generalization of the notion of vector space over a field, wherein the corresponding scalars are the elements of an arbitrary given ring and a multiplication is defined between elements of the ring and elements of the module.

Course Objective

At the end of this course the students will be able to understand the module, Cartesian product of sets, direct product and direct sum of modules, HomR(M,N), free, projective and injective module, noetherian module (both in terms of chain conditions and in terms of minimal or maximal submodules), algebra over a commutative ring, completely reducible module, semisimple ring and modules.

Course Outline

  • Elementary notions and examples,
  • Modules,
  • Submodules,
  • Quotient modules,
  • Finitely generated and cyclic modules,
  • Exact sequences and elementary notions of homological algebra,
  • Noetherian and Artinian rings and modules,
  • Radicals,
  • Semisimple rings and modules.

Text Books

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