Ring

In mathematics, a ring is an algebraic structure consisting of a set together with two binary operations (usually called addition and multiplication), where each operation combines two elements to form a third element. To qualify as a ring, the set together with its two operations must satisfy certain conditions – namely, the set must be an Abelian group under addition and a monoid under multiplication such that multiplication distributes over ad... more

In mathematics, a ring is an algebraic structure consisting of a set together with two binary operations (usually called addition and multiplication), where each operation combines two elements to form a third element. To qualify as a ring, the set together with its two operations must satisfy certain conditions – namely, the set must be an Abelian group under addition and a monoid under multiplication such that multiplication distributes over addition. While these operations are familiar from many mathematical structures, such as number systems or the integers—for example, they are also very general in the sense that they take a broad variety of mathematical objects into account. This allows one to handle entities of very different mathematical origins in a flexible way, while retaining essential structural aspects of many objects in abstract algebra and beyond. The ubiquity of rings makes them a central organizing principle of contemporary mathematics. The branch of mathematics that... less