K-monoid

𝕂-submonoid

A 𝕂-submonoid 𝐵 of an K-monoid 𝐴 is a subalgebra 𝐵 ≤𝐴 containing the identity, falg i.e. 𝐵 is itself an associative algebra; 𝐵 ⋅𝐵 ⊆𝐵 and 𝟙 ∈𝐵.

Properties

• The commutator algebra of an associative subalgebra is a Lie subalgebra

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