Ring, field, injection, surjection, bijection,

In summary, the terms ring, field, injection, surjection, bijection, jet, and bundle were introduced by various mathematicians and are translations or transliterations of words from different languages. They are used to describe mathematical structures and their properties, such as the natural numbers being associated with real things in nature. The terms were chosen based on their respective languages and origins.
  • #1
gvk
83
0
Ring, field, injection, surjection, bijection, jet, bundle.
Does anybody know who first introduced those terms and when and why those people called these matimatical structures so. I mean not the definitions but the properties of real things which can be accosiated with those mathematical structures terms.
For example, 'nutural number' is number which can be associate with the real things in the nuture, e.g. 1,2,3... Number 0 is not nutural, because nobody see zero thing, and the negative number too.
 
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  • #3
field seems to be a translation from the german of korper, and ring is pesumably also a transl;ation of something like anneau from french, or a german version.

the various jections are french transliterations.
 

What is a ring?

A ring is a mathematical structure consisting of a set of elements and two binary operations, usually called addition and multiplication. It satisfies certain axioms such as closure, associativity, and distributivity.

What is a field?

A field is a mathematical structure that is a generalization of a ring. It also consists of a set of elements and two binary operations, but with additional axioms such as the existence of multiplicative inverses for non-zero elements.

What is an injection?

An injection is a function that maps distinct elements in the domain to distinct elements in the codomain. In other words, no two elements in the domain map to the same element in the codomain.

What is a surjection?

A surjection is a function that maps every element in the codomain to at least one element in the domain. In other words, no element in the codomain is left unmapped.

What is a bijection?

A bijection is a function that is both injective and surjective. This means that every element in the domain maps to a distinct element in the codomain, and every element in the codomain is mapped to by exactly one element in the domain.

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