Definition:Algebraic System
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Definition
An algebraic system is a mathematical system $\SS = \struct {E, O}$ where:
- $E$ is a non-empty set of elements
- $O$ is a set of finitary operations on $E$.
Also known as
Some sources refer to such an object as an algebra, but the general consensus is to reserve the term algebra for a slightly more refined concept.
Also see
- Algebraic Structure: a refinement of this concept in which $O$ consists specifically of binary operations.
Sources
- 1964: W.E. Deskins: Abstract Algebra ... (previous) ... (next): $\S 1.5$
- 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): Prologue
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): algebraic system
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): algebraic system