Course Details
Subject {L-T-P / C} : MA5115 : Rings and Modules { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Dr. Ranjit Mehatari
Syllabus
Ring of continuous functions, matrix rings, polynomial rings, power series rings, Laurent rings, Boolean rings, Direct products, local rings, prime fields, Euclidean domains, PID, Unique factorization domains, Eisenstein’s criteria, modules, direct sum, free modules, quotient modules, simple modules, homomorphisms, module’s over PID’s, Artinian modules, Noetherian modules, Artian rings, Noetherian rings, Nil Radicals, Jacobson radicals.
Course Objectives
- To develop skills and to acquire knowledge on some of the basic concepts of rings and modules. To understand Theory of modules over PID and its applications.
Course Outcomes
By studying this course students will be able to explain modules and submodules and interpret all the properties of them. They will be able to understand the <br />concept of PID, UFD, Prime radical and Jacobson radical. Students will be able to define Artinian and Noetherian modules and characterize their properties.
Essential Reading
- C. Musili, Introduction to Rings and Modules, Narosa , 1994
- J. Dauns, Modules and Rings, Cambridge University Press , 1994
Supplementary Reading
- T. S. Blyth, Module Theory: An Approach To Linear Algebra, Oxford University Press , 1990
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