Definition:Algebraic System

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