English
There is an equivalence between finiteness condition of cotangent space and principal maximal ideal, expressed via a surjectivity condition.
Русский
Существует эквивалентность между условием конечной размерности котантантного пространства и главной максимальной идеалой черезSurjectivity условия.
LaTeX
$$finrank (ResidueField R) (CotangentSpace R) ≤ 1 \iff (maximalIdeal R).IsPrincipal$$
Lean4
/-- A (left) ideal in a semiring `R` is an additive submonoid `s` such that
`a * b ∈ s` whenever `b ∈ s`. If `R` is a ring, then `s` is an additive subgroup. -/
abbrev Ideal (R : Type u) [Semiring R] :=
Submodule R R
