A (commutative, unital) ring is the 3-tuple \( (R, +, \cdot) \) such that \( (R, +) \) is an Abelian group, \( (R, \cdot) \) is a commutative monoid, and the two satisfy mutually distributive laws. \( S \subset R \) is a subring of \( R \) if there exists a ring morphism \(R \to S \). An ideal \(I \subset R \) is a additive subgroup of \( R \) that absorbs all multiplication: \( \forall i \in I, r \in R: ir \in R \).

The coursework consisted of a set of exercises exploring the three, and the links between them.

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Coursework for the Abstract Algebra University of Portsmouth module.