# Definition:Algebraic System

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## Contents

## Definition

An **algebraic system** is a mathematical system $\mathcal S = \struct {E, O}$ 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): Entry:**algebraic system** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**algebraic system**