query: Algebra - Prove this is a Ring
positive_passages.docid: 23521
positive_passages.text: Power Set of $X$ is a Ring with Symmetric Difference, and Intersection
negative_passages.docid: 89702
negative_passages.text: Let $R$ be a ring such that for all $a,b$ in $R$, $(a^2-a)b=b(a^2-a)$. Then $R$ is commutative
negative_passages.docid: 83100
negative_passages.text: Prove that the center of a ring is a subring.
negative_passages.docid: 85961
negative_passages.text: Is the ring and semi-ring definition of algebra and set linked?
negative_passages.docid: 155642
negative_passages.text: Understanding divison by monic polynomial in $R[x]$ where $R$ is an arbitrary ring
negative_passages.docid: 102316
negative_passages.text: why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$
negative_passages.docid: 19310
negative_passages.text: Identify the ring $\mathbb{Z}[x]/(2x)$
negative_passages.docid: 91962
negative_passages.text: In a ring $a*a=0$ then $a+a=0$
negative_passages.docid: 154495
negative_passages.text: Prove that a nontrivial subring of a ring that is a domain has the same identity
negative_passages.docid: 14158
negative_passages.text: Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain
negative_passages.docid: 72507
negative_passages.text: Does $ab=1$ imply $ba=1$ in a ring?
negative_passages.docid: 66451
negative_passages.text: In a ring, how do we prove that a * 0 = 0?
negative_passages.docid: 127029
negative_passages.text: Ring of formal power series finitely generated as algebra?
negative_passages.docid: 126331
negative_passages.text: Associative ring with identity, inverses, divisors of zero and Artinianity
negative_passages.docid: 82953
negative_passages.text: In a ring with no zero-divisors, for $(m,n) =1$, $a^m = b^m$ and $a^n = b^n$ $\iff a =b$
negative_passages.docid: 24224
negative_passages.text: How to prove the ring of Laurent polynomials over a field is a principal ideal domain?
negative_passages.docid: 87946
negative_passages.text: Proving that the unities of a ring form a group under multiplication