center — Mathlib

English

The centralizer of a set s in A is the subalgebra consisting of all elements that commute with every element of s.

Русский

Централизатор множества s в A — подпорядок, состоящий из элементов, которые commute с каждым элементом s.

LaTeX

$$$\operatorname{centralizer}(R,s) = \{a \in A\; |\; \forall b \in s, ab = ba\}$ as a nonunital subalgebra of A$$

Lean4

/-- The center of a non-unital algebra is the set of elements which commute with every element.
They form a non-unital subalgebra. -/
def center : NonUnitalSubalgebra R A :=
  { NonUnitalSubsemiring.center A with smul_mem' := Set.smul_mem_center }

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