Rings are a popular jewelry item that can be worn for many different occasions. They can mark milestones in relationships, symbolize a promise or be worn as a token of love. They can also be adorned with charms or other talismans to bring good luck or protection. The most common rings include engagement, promise and wedding rings. They can be decorated with a variety of gemstones, inscriptions or even animal motifs. These pieces are often seen as symbols of commitment and a sign of virginity in certain religious cultures.
In the mathematical sense, a ring is a set of integers such that addition and multiplication are both additive (with inverses) and distributive. It is also an algebraic structure with the property that the multiplicative identity of an element x is equal to its additive inverse (zero is an absorbing zero-divisor). This ring has the properties of being commutative and unitary. A ring that is both commutative and unitary is called an integral domain.
A ring of rational numbers is a ring because the number of prime factors in each is finite. This is important for number theory, since factoring is a fundamental operation. The axioms of ring theory are based on the properties of arithmetic progressions and the fact that a finite number of elements cannot divide a prime number.
Other objects that are a part of ring theory are rings in topological spaces and arithmetic functions on such rings. Rings of rational numbers and algebraic functions are also important in cryptography, as they provide a way to represent and encrypt messages. A ring with a finite number of primes is a ring in topology, since its homology group is closed under pointwise addition and multiplication.
In modern jewelry, a ring is typically a band or a circle of metal or other material that wraps around the finger and can be secured with a clasp. It can be adorned with gems or other materials such as enamel, leather, wood or stone. Some of these rings are made for men, women, or both, and they may be worn on any finger. The most commonly used ring is the wedding ring, which is typically made of precious metal and is engraved with the name or initials of the couple.
Historically, rings have had several symbolic functions, including denoting marriage, exceptional achievement, high status or authority, or membership in an organization. Rings can also sport insignia, like seals or badges, and be outfitted with a secret compartment to hold items. Each finger had a traditional association or meaning for the placement of a ring, but these have become somewhat obsolete in modern times. Rings are still worn on some fingers, however, and they can be a mark of loyalty or respect. They can also be worn as a sign of affection or to make a fashion statement. Many women wear engagement and wedding rings to show their commitment to their partners. Men, on the other hand, sometimes wear multiple rings to express their style or make a statement.