query: Where does the term "Ring" come from in Algebra?
positive_passages.docid: 79641
positive_passages.text: Why are rings called rings?
negative_passages.docid: 19112
negative_passages.text: Ring $R= \mathbb Z_3[x]/\langle x^6-1\rangle$
negative_passages.docid: 24351
negative_passages.text: The ring $\Bbb Z\left [\frac{-1+\sqrt{-19}}{2}\right ]$ is not a Euclidean domain
negative_passages.docid: 150986
negative_passages.text: For a Noetherian ring $R$, we have $\text{Ass}_R(S^{-1}M)=\text{Ass}_R(M)\cap \{P:P\cap S=\emptyset\}$
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: 127029
negative_passages.text: Ring of formal power series finitely generated as algebra?
negative_passages.docid: 41398
negative_passages.text: For a ring $R$, does $\operatorname{End}_R(R)\cong R^{\mathrm{op}}$?
negative_passages.docid: 102316
negative_passages.text: why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$
negative_passages.docid: 12110
negative_passages.text: How are $2\mathbb{Z}\ncong3\mathbb{Z}$ different as rings?
negative_passages.docid: 92076
negative_passages.text: What was Newton's own explanation of Newton's rings?
negative_passages.docid: 14191
negative_passages.text: How many elements does the ring $ℤ[X]/(X^2-3,2X-4)$ have? Describe the structure of this ring.
negative_passages.docid: 4156
negative_passages.text: What is $\Bbb R^{\times}$? [unit group, ring to "times" power]
negative_passages.docid: 24247
negative_passages.text: Ring Inside an Algebraic Field Extension
negative_passages.docid: 19473
negative_passages.text: Why is quadratic integer ring defined in that way?
negative_passages.docid: 138670
negative_passages.text: If product of finite elements in a ring is a unit then can we say each element as unit
negative_passages.docid: 28327
negative_passages.text: (Simple) Examples on Non-Commutative Rings
negative_passages.docid: 52966
negative_passages.text: Rings, ideals and units-proof