supportAddSubgroup — Mathlib

English

The support AddSubgroup of a RingPreordering P is the additive subgroup consisting of all x such that x ∈ P and −x ∈ P.

Русский

Опорная подпогруппа RingPreordering P состоит из всех x, для которых x ∈ P и −x ∈ P.

LaTeX

$$$\\mathrm{supportAddSubgroup}(P) = P \\cap (-P)$$$

Lean4

/-- The support of a ring preordering `P` in a commutative ring `R` is
the set of elements `x` in `R` such that both `x` and `-x` lie in `P`.
-/
def supportAddSubgroup : AddSubgroup R where
  carrier := P ∩ -P
  zero_mem' := by aesop
  add_mem' := by aesop
  neg_mem' := by aesop

Похожие утверждения