query: A surjective ring homomorphism can map a local ring to a local ring
positive_passages.docid: 153291
positive_passages.text: Why a ring homomorphism from a local ring will not map a non-unit to a unit？
negative_passages.docid: 37058
negative_passages.text: Induced maps in homology are injective
negative_passages.docid: 42552
negative_passages.text: Localisation is isomorphic to a quotient of polynomial ring
negative_passages.docid: 32443
negative_passages.text: Find the kernel of a ring homomorphism $f(x)\to f(\sqrt 2)$
negative_passages.docid: 68728
negative_passages.text: Why does the natural ring homomorphism induce a surjective group homomorphism of units?
negative_passages.docid: 99707
negative_passages.text: free module implies surjective map of affine schemes
negative_passages.docid: 6023
negative_passages.text: Surjectivity of Composition of Surjective Functions
negative_passages.docid: 42871
negative_passages.text: Quotient of a local regular ring
negative_passages.docid: 5084
negative_passages.text: When is the completion of a ring a local ring ?
negative_passages.docid: 154847
negative_passages.text: homomorphism from $S_3$ to $\mathbb Z/3\mathbb Z$
negative_passages.docid: 129452
negative_passages.text: Groups $G,H$ with surjective homomorphisms that are quotient of each other
negative_passages.docid: 99671
negative_passages.text: Are surjective sheaf morphisms locally surjective?
negative_passages.docid: 13764
negative_passages.text: Homomorphisms from $\mathbb{Z} \rightarrow S_3$.
negative_passages.docid: 34990
negative_passages.text: Ring homomorphism defined on a field
negative_passages.docid: 30714
negative_passages.text: A question on ring homomorphisms and maximal ideals.
negative_passages.docid: 45684
negative_passages.text: Is quotient of a ring by a power of a maximal ideal local?
negative_passages.docid: 97009
negative_passages.text: Image of ring homomorphism $\phi : \mathbb{Z}[t] \to \mathbb{Q}$?