What Is a Ring?
From your marital status to your profession, the fingers you choose to wear rings on tell people a lot about you. Each finger had a specific symbolic function and association in antiquity.
A ring is an algebraic structure consisting of a non-empty set R equipped with two binary operations, addition and multiplication. Rings that satisfy commutativity for addition and multiplication are called commutative rings.
Basics
A ring is a set equipped with two operations, addition and multiplication. A ring is commutative, has additive identity and an additive inverse, and its elements are closed under multiplication. The integers are the prototypical example of a ring, and their axioms include the properties that zero is an absorbing element and that every nonzero number has an additive inverse.
The term ring also applies to the generalised algebras of any set of integers, such as the rings of real numbers, rational numbers and complex numbers. The ring of integers is a special case of such an algebra, and the ring of numbers (also called the field of numbers) plays a central role in algebraic geometry and algebraic topology.
In the field of category theory, there are structures more general than rings which are defined by similar axioms and which can be used to model different mathematical systems. Some authors use the term ring to describe such structures, while others drop the requirement for multiplication to be associative and define them as monoids or semigroups in toposes.
In algebraic topology, a ring spectrum is a monoid in a category of spectra which satisfies the ring axioms and has a unit map m : X Wedge X to X. The ring of polynomial spectra is one such ring, and the study of such rings leads to exact solution of nonlinear systems of equations.
Styles
As with all jewelry pieces, rings come in many different styles and have a variety of uses. They can be used to communicate commitments, celebrate milestones or simply express personal style. jewelry wholesale For some, rings can even convey a sense of status and wealth.
Engagement rings are the most popular type of ring and can be purchased in a wide array of designs and settings, ranging from traditional to contemporary. Other popular ring types include wedding bands, promise rings and affirmation rings. These rings can also be engraved with text or symbols that carry special meaning.
Fashion rings can be very sleek and minimal or they can feature intricate filigree work and gemstones. Some designs are inspired by specific historical eras such as Art Nouveau, Victorian or Art Deco. Others are based on organic-looking motifs like flowers, leaves and butterflies. A trending style is the halo-style ring, which features a central stone that is surrounded by a halo of smaller diamonds or gemstones to highlight its sparkle and make it appear larger.
Class rings are another common ring type. These rings can be personalized with the wearer’s initials or the insignia of their school to commemorate graduation or a special accomplishment. They can also be worn with the insignia facing forward before graduation to serve as a reminder of the journey ahead and then turned around afterward to symbolize success.
Materials
Rings can be made out of a variety of materials. Silver is a popular choice for engagement rings because of its durability and beauty. It can be polished and oxidized to take on a rich, shiny appearance.
Other metals, such as gold, can be used for wedding bands or other types of jewelry. These rings may be engraved with names, dates, or effigies of the deceased; they gold plated earrings could sport an inscription, a symbol of love or friendship (posy rings); or they could hold sentimental keepsakes in miniature, as was done with gimmel rings (Jewish marriage rings). Other kinds of rings were designed to function as talismans or amulets, such as poison rings, whose hollow bezels held poison for purposes of suicide or homicide.
Tungsten carbide is another material commonly used in rings, although it is less common for jewelry. It is harder than steel and has a more lustrous appearance, similar to platinum. This metal is scratch-resistant and durable, and it won’t rust or tarnish.
Gym rings allow for more range of motion for the joints than stationary bars, which can help reduce joint pain from weight training. These rings are also effective for building core strength and muscle tone. They also challenge the body to stay in control under tension, which is essential for success in many sports and exercises.
Symbolism
A ring is a special type of algebraic structure whose multiplication is commutative. Many of the same axioms that apply to rings also apply to other types of structures such as algebras, vector spaces and fields. However, a ring has additional properties that distinguish it from other structures. In particular, a ring must have a multiplicative identity, and its elements must be integers. For this reason, rings are often used as models for other types of structures, and most of the definitions and results in this wiki are for commutative rings.
There are other conditions that one might impose on a ring to give it special properties. For example, a ring is called a field if every nonzero element has a multiplicative inverse and addition to the ring is an identity map. Fields are fundamental objects in number theory, algebraic geometry and other areas of mathematics.
Similarly, a ring can be given a Noetherian property by imposing conditions on its ideals. For instance, a ring is left Noetherian if there exists an infinite chain of left ideals such that the inclusion map S – R S maps each element to its own multiplicative identity.
Symbols are also used in everyday life to convey meaning without having to say anything explicitly. For example, a person might wear a certain piece of jewelry as a reminder of a loved one who passed away. This is a form of symbolic behavior, and it can have very powerful effects. Some symbols are culturally specific, and they vary from place to place. For instance, a wedding proposal in Wales might be signified by “lovespoons,” while a marriage proposal in Thailand would use the word “thong mun.”