query: When can a ring be isomorphic to a quotient of itself?
positive_passages.docid: 70320
positive_passages.text: Let $R$ be a commutative Noetherian ring (with unity), and let $I$ be an ideal of $R$ such that $R/I \cong R$. Then is $I=(0)$?
negative_passages.docid: 80088
negative_passages.text: What possible characteristics may a local commutative unital ring have?
negative_passages.docid: 45523
negative_passages.text: Can the product of two non invertible elements in a ring be invertible?
negative_passages.docid: 39652
negative_passages.text: Quotient of free module
negative_passages.docid: 91129
negative_passages.text: Can there be an onto homomorphism from a ring without unity to a ring with unity?
negative_passages.docid: 129858
negative_passages.text: "Almost" ring homomorphism
negative_passages.docid: 98818
negative_passages.text: Quotient ring of a localization of a ring
negative_passages.docid: 151047
negative_passages.text: a non trivial example: $G/H$ is isomorphic to $G$
negative_passages.docid: 106894
negative_passages.text: If a subring of a ring R has identity, does R also have the identity?
negative_passages.docid: 148616
negative_passages.text: When is a ring homomorphism $A \to A$ surjective but not injective.
negative_passages.docid: 70872
negative_passages.text: Isomorphism of quotient modules implies isomorphism of submodules?
negative_passages.docid: 45684
negative_passages.text: Is quotient of a ring by a power of a maximal ideal local?
negative_passages.docid: 64025
negative_passages.text: Ring homomorphisms from $\Bbb Q$ into a ring
negative_passages.docid: 8587
negative_passages.text: What is an example of two k-algebras that are isomorphic as rings, but not as k-algebras?
negative_passages.docid: 70658
negative_passages.text: Isomorphism between quotient modules
negative_passages.docid: 34990
negative_passages.text: Ring homomorphism defined on a field
negative_passages.docid: 151993
negative_passages.text: Ring homomorphisms $\mathbb Z[x]\rightarrow \mathbb Q$