Questions tagged [abstract-algebra]
For questions about the mathematical field abstract algebra that studies algebraic structures, most notably groups, rings and fields.
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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 ...
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Who did introduce homomorphism concept for the first time?
I read that: "The term "homomorphism" appeared as early as 1892, when it was attributed to the German mathematician Felix Klein (1849–1925). Homomorphisms of vector spaces are also ...
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How did Azumaya come up with the Nakayama lemma?
Thanks to Conifold and Chris Leary's comments, I learned that the Nakayama lemma was not first created by a mathematician named Nakayama, but that mathematicians named Azumaya and Krull first created ...
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Group theory in non-European/subaltern cultures?
I'm doing undergraduate research on the history of abstract algebra (specifically permutation groups) and the notion of symmetric groups in indigenous artwork has come up several times. Is anyone ...
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Finite fields as quotients
Although finite fields are usually introduced as field extensions of fields of prime order, they also arise as quotients of number rings; e.g., $GF(9)$ comes from taking the Gaussian integers mod 3 ...
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Error-correcting codes based on Galois fields
I seem to recall reading that some French mathematician (perhaps a member of Bourbaki?) came up with the idea of basing error-correcting codes on Galois fields quite early in the development of ...
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When did mathematicians realize that theory of algebraically closed fields admits quantifier elimination?
A nice property of algebraically closed fields is that the theory that describes them ($ACF$) admits quantifier elimination: any statement can be shown equivalent (in the theory) to another statement ...
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List of textbooks on Abstract Algebra in the order of time
I am knowing Abstract Algebra things; I am searching aims of Abstract Algebra and origins of parts of Abstract Algebra. I thought original initial textbooks have explicit links to aims and origins of ...
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History behind Serre's conditions $\mathrm{S}_k$ and $\mathrm{R}_k$ for a commutative Noetherian ring
In 033Q we find defined what some sources call “Serre's conditions $\mathrm{S}_k$ and $\mathrm{R}_k$” (if you don't know what a scheme is, you can read the definition for a commutative Noetherian ring ...
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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 ...
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Where did the index of a subgroup notation $[G:H]$ begin to be used?
In texts of algebra, the cardinality of cosets is written in $[G:H]$ or $|G:H|$. Where did this notation originate?
The history about $G/H$ can be found here. $[G:H]$ is called index of a subgroup. ...
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History of group actions as their own structures
I'm interested in when (and how) the modern idea of a group action developed and how group actions became their own algebraic structures.
As far as I can tell in the 19th century group actions were ...
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How and when did the dedicated study of locally compact groups begin?
How and when did the dedicated study of locally compact groups begin?
Specific instances from literature, recorded stories, etc., may help supplement the answers. There seems to be no reason why I ...
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Intuitions for Frobenius' generalization of characters to nonabelian finite group given the historical context
I'm reading about the history of character theory of finite group, especially about the invention of character theory by Frobenius.
According to most of the related papers (e.g. Pioneers of ...
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Why is the ring of algebraic integers denoted by $\mathcal O_K$?
Why/when was the curly-O notation chosen for the ring of integers of an algebraic number field $K$?
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