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Abstract Algebra I (Groups and Rings)

This text introduces two theories in abstract algebra: group theory and ring theory. Topics covered include Cosets and Lagrange’s Theorem, isomorphism theorems, classification of abelian groups, polynomial rings and Euclidean division, accompanied by numerous worked examples and detailed step-by-step explanations. Readers may review their knowledge by attempting the exercise chapters following each theory. Solutions are provided....

Keywords:: Cosets and Lagrange’s Theorem, Group Theory, ASEAN University Network, Polynomial Rings, NTU Singapore, AUN, Isomorphism Theorems, Abstract Algebra, Ring Theory

Disciplines:

Mathematics and Statistics / Mathematics / Algebra and Number Theory / Abstract Algebra

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Material Type:: Open (Access) Textbook
Date Added to MERLOT:: November 28, 2025
Date Modified in MERLOT:: December 2, 2025
Author:: Frederique Oggier, Nanyang Technological University, Singapore
Submitter:: Charlotte Choo
Primary Audience:: College General Ed, College Lower Division
Technical Format:: PDF, Website

Mobile Compatibility:: Not specified at this time
Language:: English
Cost Involved:: No
Source Code Available:: Unknown
Creative Commons:: This work is licensed under a Attribution-NonCommercial-NoDerivatives 4.0 International

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Abstract Algebra I (Groups and Rings)

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