- #1
gvk
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Does anybody know who first introduced terms ring and field and when?
The Origin & History of Ring & Field: Who Invented Them?
In summary, Richard Dedekind is credited with introducing the terms "ring" and "field" in the late 1850s. However, there is some debate about the translation of his term "korper" with some sources attributing the English term "field" to Eliakim Hastings Moore. The term "ring" seems to be both an English and German word, possibly due to its use in Wagner's operas.
- #2
HallsofIvy
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I put "mathemtics" "terms" "history" into Google and came up with this intersting site:
http://members.aol.com/jeff570/mathword.html
According to it, it was Richard Dedekind who introduced both terms in the late 1850s.
http://members.aol.com/jeff570/mathword.html
According to it, it was Richard Dedekind who introduced both terms in the late 1850s.
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- #3
gvk
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Thank you, very handy website 
- #4
mathwonk
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technically, it appears the website mentioned states that eliakim hastings moore introduced the english term "field", as dedekind's term "korper" apparently translates literally as "body" rather than field.
I do not have a german dictionary handy though. Is perhaps "field" another translation of "korper"? interestingly "ring" seems to be both an english and a german word, as used in wagner's famous operas. or is this wrong?
I do not have a german dictionary handy though. Is perhaps "field" another translation of "korper"? interestingly "ring" seems to be both an english and a german word, as used in wagner's famous operas. or is this wrong?
Related to The Origin & History of Ring & Field: Who Invented Them?
1. What is the origin of rings and fields?
The concept of rings and fields originated in the field of abstract algebra, which emerged in the early 19th century. Mathematicians such as Richard Dedekind, Ernst Kummer, and Leopold Kronecker contributed to the development of these mathematical structures.
2. Who invented rings and fields?
While many mathematicians played a role in the development of rings and fields, the concept was first formally defined by German mathematician Richard Dedekind in the late 19th century. Dedekind introduced the concept of an "ideal" in algebra, which laid the foundation for the modern understanding of rings and fields.
3. What is the difference between a ring and a field?
A ring is a mathematical structure that consists of a set of elements and two binary operations (usually addition and multiplication) that satisfy certain properties. A field is a special type of ring in which all non-zero elements have a multiplicative inverse. In simpler terms, a field is a more specific and "complete" version of a ring.
4. How are rings and fields used in mathematics?
Rings and fields have many applications in mathematics, particularly in abstract algebra and number theory. They are also used in other fields such as geometry, physics, and computer science. For example, fields are essential for coding theory and cryptography, while rings are used in the study of polynomial equations.
5. Are rings and fields still relevant in modern mathematics?
Absolutely! Rings and fields are fundamental mathematical structures that continue to be used extensively in various areas of mathematics and beyond. They provide a powerful framework for understanding and solving complex problems, and their applications are constantly expanding as new discoveries are made in mathematics and other fields.
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