What Is a Ring?

A ring is a circular band, usually made of metal, worn as ornamental jewellery, either alone or in combination with other materials such as gemstones and plastic. A ring may be worn around the finger or other parts of the body, such as the toe or arm. The term ring is also used for a set of interlocking rings that form one unit; this class of objects is important in number theory and algebraic geometry.

Throughout history, rings have been a symbol of love and commitment in many cultures. Engagement and wedding rings are common examples, as are rings worn to signify loyalty in other social groups, such as the military or law enforcement. Rings have also been used as symbols of wealth, status, and power.

There is a wide range of ring prices available, depending on the size, material, and embellishments. A simple band might cost a few hundred dollars, while a large diamond could be priced in the thousands of dollars. Some ring styles include precious stones, such as sapphires or rubies. Others have intricate metalwork designs or engravings. The inscriptions on rings can reveal personal information about the wearer.

Astrology has long held that the ring finger, which is located on the active hand (Sun), is a key link in our energy system and can be a source of communication and connection with others. Some people use a ring to bring positive changes into their lives, such as attracting money or improving health. It is generally recommended that the ring be worn with a gem of a deep color to increase its power and effectiveness.

The study of rings began with the work of Emmy Noether. Her definition of a ring included the following properties: a ring has additive and multiplicative identities, additive and multiplicative inverses, addition is commutative, and multiplication is associative. This work was further developed by Birkhoff and Mac Lane, who introduced the notion of centralizers and commutants.

A ring is a fundamental object in algebraic number theory and algebraic geometry, as well as other areas of mathematics. The study of rings can lead to the development of new algebraic structures and solve a variety of problems in these fields.

A ring is any set equipped with the operations of addition and multiplication, and satisfies certain other properties: it is compact, closed, bounded, additive, multiplicative, and symmetrical. Most books on algebra, up to 1960, followed Noether’s convention of not requiring 1 in the definition of a ring. However, since then it has become increasingly common to require that a ring have a unit element. Some authors, such as Artin and Bourbaki, depart from this convention, defining a ring to be a field. Fields are commutative and have a multiplicative inverse, but not all rings have this property.