query: $(A+, \cdot)$ finite ring. If $(ab-1)b = 0$, then $b(ab-1) = 0$
positive_passages.docid: 157863
positive_passages.text: A finite pseudo-ring such that $ab^2=b$ for some $(a,b)\in A$
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: 14343
negative_passages.text: Every nonzero element in a finite ring is either a unit or a zero divisor
negative_passages.docid: 6128
negative_passages.text: If $a \cdot a = 1$ then $a = 1$ or $a = -1$
negative_passages.docid: 14055
negative_passages.text: How to show that a finite commutative ring without zero divisors is a field?
negative_passages.docid: 21840
negative_passages.text: Zero divisors and units for the ring $\mathbb{Z}/n\mathbb{Z}$ with integer $n$
negative_passages.docid: 150309
negative_passages.text: Why do we assume $a+b=b+a$ in a Ring with 1. Also, is it true with Rings without 1?
negative_passages.docid: 107207
negative_passages.text: $A\subseteq B\subseteq C$ ring extensions, $A\subseteq C$ finite/finitely-generated $\Rightarrow$ $A\subseteq B$ finite/finitely-generated?
negative_passages.docid: 114688
negative_passages.text: Show that a division ring is simple.
negative_passages.docid: 107454
negative_passages.text: Why D/I is finite if I is a non-zero ideal of the ring of integers of a number field?
negative_passages.docid: 8589
negative_passages.text: $\sqrt[b_1]{a_1}+\sqrt[b_2]{a_2}+\cdots+\sqrt[b_k]{a_k}$ not an integer
negative_passages.docid: 64108
negative_passages.text: how to prove $a+b-ab \le 1$ if $a,b \in [0,1]$?
negative_passages.docid: 130073
negative_passages.text: $N(ab) \geq N(a)$ is not necessary for the ring to be euclidean
negative_passages.docid: 81296
negative_passages.text: If A and B are ideals of a ring, show that A + B = $\{a+b|a \in A, b \in B\}$ is an ideal
negative_passages.docid: 62012
negative_passages.text: What is $0\div0\cdot0$?
negative_passages.docid: 77198
negative_passages.text: Showing that the characteristic of a commutative ring R without zero divisors is 0 or prime
negative_passages.docid: 78350
negative_passages.text: When does a finite ring become a finite field?