Normal submonoid

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ANALOGY: This is an analogue in monoid of a property encountered in group. Specifically, it is a submonoid property analogous to the subgroup property: normal subgroup
View other analogues of normal subgroup | View other analogues in monoids of subgroup properties (OR, View as a tabulated list)

Definition

A submonoid H of a monoid M is said to be normal if Hx = xH \forall x \in M.

Analogy

The notion of normal submonoid is the generalization to monoids of the notion of normality for subgroups. Recall that a subgroup H of a group M is said to be normal if xH = Hx \forall x \in M.