Rings and Fields - Introductory Abstract Algebra
[UI, Ibadan] MAT 211/213: Abstract AlgebraThis learning track brings together the essential building blocks of abstract algebra in one clear, structured path.
We begin with the fundamentals—set theory, relations, and mappings—to build the logical foundation for working with algebraic systems. Then we move into binary operations, groups, subgroups, and homomorphisms, helping you develop the tools to recognize structure and symmetry. The track wraps up with rings, fields, and key ideas from elementary number theory that tie everything together.
Curated for second-year undergraduates in engineering and physical sciences at the University of Ibadan, but equally valuable for any learner stepping into abstract algebra for the first time. Clear, focused, and paced to guide you with both depth and intuition.
This learning track brings together the essential building blocks of abstract algebra in one clear, structured path. We begin with the fundamentals—set theory, relations, and mappings—to build the logical foundation for working with algebraic systems. Then we move into binary operations, groups, subgroups, and homomorphisms, helping you develop the tools to recognize structure and symmetry. The track wraps up with rings, fields, and key ideas from elementary number theory that tie everything together. Curated for second-year undergraduates in engineering and physical sciences at the University of Ibadan, but equally valuable for any learner stepping into abstract algebra for the first time. Clear, focused, and paced to guide you with both depth and intuition.
Course Chapters
1Introduction
Definition of a ring, ring axioms, properties, examples.
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2Some Special Rings
Commutative rings, Boolean rings, integral domains - properties and examples.
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3Subrings
Definition, subring test, and illustrative examples; two-sided ideals.
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4Ring Homomorphisms
Definition and illustration of ring homomorphisms.
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5Fields
Division rings, fields - definition, properties and illustrative examples.
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