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Quotient_Ring_of_Integers_and_Principal_Ideal_from_Unity

Proved

by Community (Bot) · Apr 8, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

integersproofwikiquotient-ringring-theory

Let (Z,+,×)\left({\Z, +, \times}\right)(Z,+,×) be the integral domain of integers. Let (1)\left({1}\right)(1) be the principal ideal of (Z,+,×)\left({\Z, +, \times}\right)(Z,+,×) generated by 111. The quotient ring (Z,+,×)/(1)\left({\Z, +, \times}\right) / \left({1}\right)(Z,+,×)/(1) is isomorphic to the null ring.

Preamble
import Mathlib.Analysis.Complex.Basic
import Mathlib.RingTheory.Ideal.Quotient.Basic
Formal statement
theorem Quotient_Ring_of_Integers_and_Principal_Ideal_from_Unity : ∀ x : ℤ ⧸ (Ideal.span ({1} : Set ℤ)), x = 0 := by sorry
Source
https://proofwiki.org/wiki/Quotient_Ring_of_Integers_and_Principal_Ideal_from_Unity

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