On the theorem of Gelfand–Mazur. New blog post on Freedom Math Dance

I discuss several elementary proofs of this theorem that I learned by browsing at the online Bourbaki archives. They are due to Tornheim and Witt.

https://freedommathdance.blogspot.com/2026/04/on-theorem-of-gelfand-mazur.html

#math #bourbaki #FreedomMathDance

#FreedomMathDance
New blog post : Associated prime ideals

I discuss the first results in the theory of associated prime ideals of modules over arbitrary rings. You'll see that a small variation in the definition can simultaneously free us of hypotheses and make the proofs simpler…

https://freedommathdance.blogspot.com/2023/02/associated-prime-ideals.html

The Klein group, the centralizer of a permutation, and its relation with the alternating group.

New blog post at #FreedomMathDance

#algebra #Vierergruppe #Klein #signature #permutation #combinatorics

https://freedommathdance.blogspot.com/2023/01/the-klein-group-and-centralizer-of.html

Blog post on #FreedomMathDance:
On positive real numbers, the choice of a the positive square root gives rise to a multiplicative square root: one has √(𝑎𝑏)=√𝑎·√𝑏 . In this blog post, I discuss (part of) a paper by William Waterhouse about when such multiplicative square roots do exist, and when they don't.

https://freedommathdance.blogspot.com/2022/12/multiplicative-square-roots.html