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Let $A$ be a commutative ring with unity. Let $f: A \to {\mathbb{Z}}/2$ be a ring homomorphism to the integers modulo 2. When does there exist a lift $g: A \to {\mathbb{Z}}$ to the integers such that $f(x)$ is the residue of $g(x)$ modulo 2 whenever $x$ in $A$?

  • The question is way too broad. For example if $A=\mathbb{Z}[x_1,\dotsc,x_n]/(f_1,\dotsc,f_r)$ you ask when a solution of a polynomial system over $\mathbb{F}_2$ can be lifted to a solution over $\mathbb{Z}$, which undecidable. – Martin Brandenburg Mar 08 '14 at 20:01
  • This question may be "too broad" mathematically, but that doesn't mean it should be closed as "too broad" for this site. The explanation text is this: There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs. If @MartinBrandenburg posted his comment as an answer, I think we would have a sufficient answer to this question in much less than a few paragraphs. – Caleb Stanford Mar 08 '14 at 21:02
  • Point being, "too broad" means a different thing mathematically than it does as a closure reason. – Caleb Stanford Mar 08 '14 at 21:02
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    General blabla doesn't help anyone. There is just nothing which can be said about this question. – Martin Brandenburg Mar 08 '14 at 22:01

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