What Is a Ring?


Rings are circular objects that can be worn around a finger. They can be made of metal or other materials, and they may have gemstones in them. People wear rings for a variety of reasons. They can be a symbol of love or commitment, they can be a status symbol, and they can also be used to signify religious or cultural beliefs. In some cultures, rings are also worn as a protection against evil spirits or bad luck.

The rings of Saturn, which are composed of bits of ice and rock, are the best known example of such an object. Other gas giants, including Jupiter and Neptune, have rings as well. The rings of Neptune are very faint and dusty, however.

In mathematics, a ring is a structured object that has a simpler structure than a complete local field. It satisfies the axioms of commutative algebra and algebraic geometry, such as ring addition is additive and ring multiplication is commutative. For convenience, books on commutative algebra or algebraic geometry usually use the term “ring” to mean a commutative ring.

Unlike fields, a ring does not require multiplicative identity for its components or for its elements to have a multiplicative inverse. This is important because it enables a simple proof that rings are abelian groups, which have properties that make them very useful in representation theory and cryptography.

When a ring is not commutative, it is not necessarily an algebraic ring; for example, the set of even integers does not satisfy the axioms of a ring because ab does not necessarily equal ba. The terminology of a ring in physics or mathematics is usually simplified to exclude non-commutative rings, since these tend to be less useful in practice.

A ring is typically formed from the intersection of a line segment with itself, which has an inscribed circle and a radius of infinity. It can also be defined by a set of points, which are called its vectors, and an inscribed triangle whose sides are the lines joining these points to the origin. A ring is called closed if its ends meet and open if its edges do not meet.

The ring of Lord Sauron was the source of all evil in The Hobbit movies, but Frodo possessed a strong will and defeated it. The ring could have corrupted him and turned him into Sauron, but because of his good will, the ring remained in his possession and did not destroy him. Similarly, rings can be used to enhance your own power and will. A ring can be used to increase energy, stimulate intellect and enhance creativity, among other things. This is why some men choose to wear multiple rings on each finger. They can be stacked for a cluttered, rock n’ roll look, or coordinated to reflect symbolic meaning or the position of each ring on their hand. This is a great way to express personal style. It also shows confidence and strength.