All Questions
Tagged with terminology abstract-algebra
20
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The Root of a Geometric Progression
Good people!
I'm presently in the process of putting something together on Euler and Gauss and cyclotomy and modular arithmetic, and I noticed that when it comes to the terminology primitive root ...
- 445
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1
answer
132
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When did Macaulay rings become Cohen-Macaulay rings?
In his book on commutative rings (published 1970), Kaplansky talks about Macaulay rings. In the mid 1970's, I learned some commutative algebra from a student of his, who referred to these rings as ...
- 218
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2
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206
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Why is it called a group action?
A group action has two laws which roughly correspond to associativity and identity
$
\phi : (G : \textrm{Group}) \times (S : \textrm{Set}) \rightarrow S \\
\forall a, b : G . \forall c : S. \phi(a,\...
7
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1
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350
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Why is the number of elements in a group called "order"?
This is a question that I have for a long time, Maybe it is something silly, but I really want to know. Why is the number of elements in a group called "order"? I mean, the word "order&...
- 181
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429
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Could a "field" have non-commutative multiplication originally?
Today, when the term "field" is defined in algebra, it is almost always stipulated that all fields are commutative. However, the author of these lectures says that this has not always been ...
- 63
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Origin of the term 'index of a subgroup'
The index of a subgroup $H$ in a group $G$ is the number of distinct cosets of $H$ in $G$.
Why did someone decide to call this an 'index'?
- 151
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40
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History of Path algebras
I want some references that point the inventor of Path algebras and history/evolution of these algebras from the first idea. If possible.
I tried to search in many different places, but all times, ...
10
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1
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550
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How did the terms "center" and "centralizer" come up in group theory?
Usually the word center means the center of a circle. I have encountered the word center in group theory, but do not see any connection with the center of a circle. I think the history of group theory ...
- 203
2
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1
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History of group theory character tables (as used in physics and chemistry)
Does anyone know who started using the symbols A, B, E, T (First column, left) for showing irreducible representations of symmetry groups? In older maths books I see capital gamma. Herein A= totally ...
- 4,184
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Where does the letter S in "$S$-units" and in localization $S^{-1} R$ come from?
In number theory, we may encounter the notion of $S$-unit, $S$-integer, etc. where $S$ is a finite set of prime numbers (for simplicity). For instance, if $S = \{2,3\}$ then the $S$-integers are the ...
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What was the significance of Eisenstein's discovery of invariants?
I am trying to decipher a portion of James Joseph Sylvester's 1869 address entitled "The Study That Knows Nothing of Observation", which, among other things, surveys the landscape of 19th century ...
- 477
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460
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Whence “homomorphism”, “homomorphic”?
The kernel question leads to another : Today, homomorphism (resp. isomorphism) means what Jordan (1870) had called isomorphism (resp. holoedric isomorphism). How did the switch happen?
“Homomorphic” ...
- 7,764
3
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1
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252
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Why is the term "kernel" used in algebra? [duplicate]
What was the motivation to use the word "kernel" in algebra to denote the set of all arguments which are mapped to the idendity element (by a homomorphism)? Who introduced it?
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9
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1
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633
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Who was first to differentiate between prime and irreducible elements?
I recently learned about irreducible and prime elements in a commutative ring. However, my professor was not quite sure who was the first to make this distinction, or give an example of an irreducible ...
- 113
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516
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What is the origin of "an algebra" as in vector space with multiplication?
What is the origin of calling a vector space over a field $F$ endowed with multiplication an algebra? Tried searching, but not surprisingly Google likes to drop the article and just bring me to the ...
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