Definition:Subsemigroup
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Definition
A subsemigroup $\left({T, \circ}\right)$ of an algebraic structure $\left({S, \circ}\right)$ is a semigroup $\left({T, \circ}\right)$ such that $T \subseteq S$.
Need to use something like $\ast = \circ\restriction_{T \times T}$ instead; $\circ$ is formally not a binary operation on $T$
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We write:
- $\left({T, \circ}\right) \subseteq \left({S, \circ}\right)$
Sources
- Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 8$
- Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 32$
