Group Ring

A group ring is a mathematical structure that combines two concepts: groups and rings. Think of it as a way to create a new system where elements of a group (a set with an operation like addition or multiplication) are combined with coefficients from a ring (like integers or real numbers). In a group ring, elements are formal sums where each group element is multiplied by a coefficient from the ring. This construction allows mathematicians to study group properties within an algebraic framework, enabling applications in areas like representation theory and algebraic topology.