Unit I
Rings and Ideals, Modules and operations on them (tensor product, Direct sum and product)
| Course Name | Commutative Algebra |
| Course Code | 24MAT431 |
| Program | 5 Year Integrated MSc/ BSc. (H) in Mathematics with Minor in Data Science |
| Semester | Elective |
| Credits | 3 |
| Campus | Amritapuri |
Rings and Ideals, Modules and operations on them (tensor product, Direct sum and product)
Rings and modules of Fractions, primary decomposition.
Integral dependence and Valuations, Chain Conditions.
Noetherian Rings and Artin Rings.
Discrete valuation Rings and Dedekind Domains, Dimension theory.
Course Outcomes:
CO-1: To understand the basic definitions of rings, ideals and modules through examples; To construct new modules by tensor product, Hom, direct sum/product.
CO-2: To understand the fractions of modules and apply the fractions to construct the field from integral domain. To familiarize the decomposition of rings/modules.
CO-3: To familiarize the concept of integral dependence of extension ring and chain conditions of modules. To understand the definitions of valuations / Noetherian / Artin rings through examples.
CO-4: To study the basic properties of Noetherian/Artin rings; use the basic properties to characterize/decompose the Noetherian/Artin rings.
CO-5: To understand the basic definitions of discrete valuation rings and Dedekind domains.
To familiarize the concept of dimension theory of rings/modules.
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