# Category:Subsemigroups

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This category contains results about **Subsemigroups**.

Definitions specific to this category can be found in **Definitions/Subsemigroups**.

Let $\struct {S, \circ}$ be an algebraic structure.

Let $T \subseteq S$ such that $\struct {T, \circ {\restriction_T} }$, where $\circ {\restriction_T}$ is the restriction of $\circ$ to $T$, is a semigroup.

Then $\struct {T, \circ {\restriction_T} }$ is a **subsemigroup** of $S$.

## Subcategories

This category has the following 4 subcategories, out of 4 total.

## Pages in category "Subsemigroups"

The following 18 pages are in this category, out of 18 total.

### G

### I

### S

- Semigroup is Subsemigroup of Itself
- Set of Associating Elements forms Subsemigroup of Magma
- Set of Subgroups of Abelian Group form Subsemigroup of Power Structure
- Set of Subsemigroups forms Complete Lattice
- Set of Subsemigroups of Commutative Semigroup form Subsemigroup of Power Structure
- Subsemigroup Closure Test
- Subsemigroup of Monoid is not necessarily Monoid