The Definition of Rings in Mathematics


A ring is a circular band of precious or decorative metal, or a piece of string, worn around the finger (see also earring). Rings have been used since ancient times to adorn the hand and other parts of the body, and have been a status symbol in societies all over the world. In modern times, they are worn mainly for ornamental purposes and to signify a commitment to a partner or to a cause. The emergence of a formal definition of rings in mathematics spanned the 1870s to 1920s, with contributions by Dedekind, Hilbert, Fraenkel, and Noether. Rings are important objects in number theory, algebraic geometry, and other branches of mathematics.

A key property of a ring is that it is commutative, meaning that for all elements in the ring, the operation of addition and multiplication is commutative. Examples of commutative rings include the set of integers, the ring of polynomials, the coordinate ring of an affine algebraic variety, and the ring of integers of a number field. Noncommutative rings are more general: they can contain n-by-n real square matrices, group rings in representation theory, operator algebras in functional analysis, and cohomology rings in topology.

Some authors define a ring more generally, in terms of the topology of its element sets. This is a more general form of the field, and it allows for a much wider range of rings to be defined. The definitions are not entirely consistent with each other, and some authors use the term field to refer only to the more general commutative and associative rings.

The planetary rings that surround the outermost planets of our solar system are fascinating, and scientists have come up with two main theories to explain their origin. One is that the rings are the remains of a shattered moon, which was broken apart by a passing comet or by tidal forces from other surrounding moons.

Another theory suggests that the rings are made of particles ejected from a star by a violent collision with a massive planet or an object. These particles then agglomerated and dispersed into thin disks.

Regardless of their origin, the fact that ring structures are so stable is remarkable. Many rings are now being discovered in our galaxy, and researchers are hoping to learn more about them by studying the collisions of stars in our galactic neighborhood.

Measuring ring size

For accurate ring sizing, it’s a good idea to warm up your hands before taking the measurement. Getting your ring size measured is easy; simply take a length of string and wrap it around the base of your finger where you’ll wear the ring, and mark the spot where the ends of the string overlap. Then use a ruler to measure the length of the string to determine your ring size.

When choosing a ring, it’s best to err on the side of a slightly larger size. This will allow for a little bit of give in the knuckle throughout the day and account for natural finger shrinkage that happens each month for many women.