Definition:Algebraic Structure
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Definition
An algebraic structure is a set $S$ which has one or more binary operations $\circ_1, \circ_2, \ldots, \circ_n$ defined on all the elements of $S \times S$, and is denoted $\left({S, \circ_1, \circ_2, \ldots, \circ_n}\right)$.
$\left({S, \circ}\right)$ or $\left({T, *}\right)$, etc. are the symbols usually used for the general algebraic structure with one (binary) operation.
Sources
- J.A. Green: Sets and Groups (1965)... (previous)... (next): $\S 4.4$
- Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 6$
- Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 26$
