query: Does a homomorphism of rings always send ideals into ideals?
positive_passages.docid: 153984
positive_passages.text: The direct image of an ideal need not be an ideal
negative_passages.docid: 126644
negative_passages.text: Simple module and homomorphisms
negative_passages.docid: 642
negative_passages.text: Does a surjective ring homomorphism have to be surjective on the unit groups?
negative_passages.docid: 22604
negative_passages.text: Can $R \times R$ be isomorphic to $R$ as rings?
negative_passages.docid: 90314
negative_passages.text: Maximal ideals in $R[x]$
negative_passages.docid: 45684
negative_passages.text: Is quotient of a ring by a power of a maximal ideal local?
negative_passages.docid: 27670
negative_passages.text: Group homomorphisms $\mathbb{Q}\to\mathbb{R}$
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: 70872
negative_passages.text: Isomorphism of quotient modules implies isomorphism of submodules?
negative_passages.docid: 111743
negative_passages.text: In a ring homomorphism we always have $f(1)=1$?
negative_passages.docid: 47114
negative_passages.text: What is necessary and/or sufficient for polynomials to provide isomorphic quotient rings?
negative_passages.docid: 55900
negative_passages.text: Is there a ring homomorphism $M_2(\mathbb Z)\to \mathbb Z$?
negative_passages.docid: 112131
negative_passages.text: Characterizing all ring homomorphisms $C[0,1]\to\mathbb{R}$.
negative_passages.docid: 121244
negative_passages.text: Homomorphisms and automorphisms on polynomial rings
negative_passages.docid: 157378
negative_passages.text: On an injective ring homomorphism from the ring of continuous functions to the ring of differentiable functions
negative_passages.docid: 78350
negative_passages.text: When does a finite ring become a finite field?
negative_passages.docid: 140557
negative_passages.text: Counting ring homomorphisms from $\mathbb{Z}[x,y]/(x^3+y^2-1)$ to $\mathbb{Z_7}$