Abstract Algebra

Checkpoints

• Field Basis A field is a commutative ring in which every non-zero element has a multiplicative inverse — division is always possible. This article defines fields, surveys the key examples, and introduces the concept of characteristic.
• Group Basis A group is a monoid where every element is reversible — every operation can be undone. This article defines groups, works through concrete examples, and introduces abelian groups.
• Ring Basis A ring is a set equipped with two operations — addition and multiplication — linked by distributivity. This article defines rings, explores concrete examples, and distinguishes commutative from non-commutative rings.