Let $R$ be a ring such that $a^5=a$ for all $a \in R$. Then it follows that $R$ is commutative. This is part of a more general well-known theorem by Jacobson for arbitrary exponents ($a^n=a$), which appeared on math.stackexchange a couple of times. But what I would like to see is a proof which is […]

This question already has an answer here: Has any previously unknown result been proven by an automated theorem prover? 8 answers

The Wikipedia page on automated theorem proving states: Despite these theoretical limits, in practice, theorem provers can solve many hard problems… However it is not clear whether these ‘hard problems’ are new. Do computer-generated proofs contribute anything to ‘human-generated’ mathematics? I am aware of the four-color theorem but as mentioned on the Wikipedia page, perhaps […]

A monoid is a set $S$ together with a binary operation $\cdot:S \times S \rightarrow S$ such that: The binary operation $\cdot$ is associative, that is, $(a\cdot b) \cdot c=a\cdot (b \cdot c)$ for all $a,b,c \in S$. There is an identity element $e \in S$, that is, there exists $e \in S$ such that […]

Intereting Posts

Arbitrary intersection of closed, connected subsets of a compact space connected?
Chinese Remainder Theorem Explanation
How to expand $\sqrt{x^6+1}$ using Maclaurin's series
Product of cosines: $ \prod_{r=1}^{7} \cos \left(\frac{r\pi}{15}\right) $
Intuition for uniform continuity of a function on $\mathbb{R}$
Asymptotic expansion of an integral
polynomial values take on arbitrarily large prime factors?
What is the fastest way to find the characteristic polynomial of a matrix?
How to learn commutative algebra?
Existence and Uniqueness Theorem
Polynomials representing primes
union of two independent probabilistic event
How many ways are there to divide $100$ different balls into $5$ different boxes so the last $2$ boxes contains even number of balls?
Can $\ln(x)=\lim_{n\to\infty} n\left(x^{\frac1{n}}-1 \right)$ be expressed as an infinite telescoping product?
The sum of the first $n$ squares is a square: a system of two Pell-type-equations