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Theorems · Definition · nonassociative algebras

SymAlg

Type u_1 → Type u_1

The symmetrized algebra (denoted as αˢʸᵐ) has the same underlying space as the original algebra α.

Defined in
Mathlib.Algebra.Symmetrized
Cited by
43 results in Mathlib
Foundations
Depth 0 from the axioms · uses no axioms
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SymAlg.sym · cited by 26SymAlg.symSymAlg.unsym · cited by 25SymAlg.unsymSymAlg.sym_injective · cited by 3SymAlg.sym_injectiveSymAlg.unsym_injective · cited by 3SymAlg.unsym_injectiveSymAlg.mul_def · cited by 2SymAlg.mul_defSymAlg.sym_eq_one_iff · cited by 1SymAlg.sym_eq_one_iffSymAlg.sym_eq_zero_iff · cited by 1SymAlg.sym_eq_zero_iffSymAlg.sym_mul_sym · cited by 1SymAlg.sym_mul_symSymAlg.unsym_eq_one_iff · cited by 1SymAlg.unsym_eq_one_iffSymAlg.unsym_eq_zero_iff · cited by 1SymAlg.unsym_eq_zero_iffSymAlg.unsym_sym · cited by 1SymAlg.unsym_symSymAlg.invOf_sym · cited by 0SymAlg.invOf_symSymAlg.mul_comm · cited by 0SymAlg.mul_commSymAlg.sym_add · cited by 0SymAlg.sym_addSymAlg.sym_bijective · cited by 0SymAlg.sym_bijectiveSymAlgCITED BYCITES

Cites0

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Nothing in Mathlib beyond the foundations.

Cited by45

Results whose statement or proof uses this declaration.