query: Show finite ring has identity when for each $x$ there exists $y$ such that $xyx = x$.
positive_passages.docid: 147332
positive_passages.text: A finite von Neumann regular ring is unital and has $ab = 1$ if $ba = 1$
negative_passages.docid: 125174
negative_passages.text: Combinatorial intuition of identity
negative_passages.docid: 63568
negative_passages.text: Ring with finitely many zerodivisors
negative_passages.docid: 144105
negative_passages.text: Ring homomorphism from $\mathbb Z$ to $\mathbb Z$ is always identity or $0$
negative_passages.docid: 16643
negative_passages.text: A slick proof that a field which is finitely generated as a ring is finite
negative_passages.docid: 92583
negative_passages.text: Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
negative_passages.docid: 114522
negative_passages.text: Prove that identity is unique in a group
negative_passages.docid: 1251
negative_passages.text: If $[G:K]$ is finite, then $[H:H \cap K] = [G:K]$ iff $G = HK$ (Hungerford Proposition 4.8, Proof)
negative_passages.docid: 85913
negative_passages.text: R is commutative ring with identity & define $\circ$ on $R$ by for any $a,b \in R$ $a \circ b=a+b-ab$ Prove the following
negative_passages.docid: 145397
negative_passages.text: How to prove that for every $i$, $a_i = i$
negative_passages.docid: 145873
negative_passages.text: Let $X$ and $Y$ be finite sets. Then the set $Y^X$ is finite and $\#(Y^X) = (\#Y)^{\#X}$.
negative_passages.docid: 62077
negative_passages.text: Prove that if $W_1\subseteq V$ finite-dimensional, then there is $W_2\subseteq V$ such that $V=W_1\oplus W_2$
negative_passages.docid: 144789
negative_passages.text: identify the ring $\mathbb{Z}[x]/(2x-1)$
negative_passages.docid: 149856
negative_passages.text: Image of ring homomorphism is a subring
negative_passages.docid: 18971
negative_passages.text: Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$
negative_passages.docid: 93632
negative_passages.text: Existence of a ring homomorphism implies characteristic divisibility
negative_passages.docid: 84149
negative_passages.text: Prove that an infinite ring with finite quotient rings is an integral domain