Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 adj. Of, relating to, or designating algebra.
 adj. Designating an expression, equation, or function in which only numbers, letters, and arithmetic operations are contained or used.
 adj. Indicating or restricted to a finite number of operations involving algebra.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Of, or relating to, algebra.
 adj. Containing only numbers, letters, and arithmetic operators.
 adj. (said of a number) Which is a root of some polynomial whose coefficients are rational.
 adj. Describing squares by file (referred to in intrinsic order rather than by the piece starting on that file) and rank, both with reference to a fixed point rather than a playerdependent perspective.
from the GNU version of the Collaborative International Dictionary of English
 adj. Of or pertaining to algebra; using algebra; according to the laws of algebra; containing an operation of algebra, or deduced from such operation
 adj. progressing by constant multiplicatory factors;  of a series of numbers. Contrasted to
arithmetical .
from The Century Dictionary and Cyclopedia
 Pertaining to algebra.
 Involving no operations except addition, subtraction, multiplication, division, and the raising of quantities to powers whose exponents are commensurable quantities: as, an algebraic equation or expression.
 Relating to the system of quantity which extends indefinitely below as well as above zero.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adj. of or relating to algebra
Etymologies
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Examples

Solow's models converged with what I was learning in algebraic topology.

This is, indeed, what they are, if we take the word algebraic in a loose enough sense.

Real numbers that are solutions of polynomial equations with integer coefficients are called algebraic, and the search was on for numbers that are not algebraic.

This idea that there is some group of "logical functions" whose repeated application to some other entities yield complex propositions (and relations) is characteristic of what I am calling algebraic approaches.

Yet she had apparently taken him, as women will, for better, for worse, till death, as trustfully as if he and men generally were as knowable as A B C, instead of as unknown as the algebraic X.

At Bath, he will be working with Professor Gregory Sankaran in the branch of mathematics known as algebraic geometry.

FOOTNOTES TO ALGEBRA whose title was inspired by Marne Kilates who once published some of my poems in his lovely poets Picturebook and called them "algebraic" should come out later this year.

It's for a socalled "Poetry and Math" issue and Marne thought my poems were "algebraic"...then notes in his Editor's Intro that I have an M.B.A.

We will see below that others hold similar "algebraic" conceptions of propositions, where the propositions are complex entities consisting of constituents bound together in certain ways and so are structured propositions.

They found the music stupid, devoid of melody and form, and bristling with "algebraic" harmonies.
Lippincott's Magazine, Vol. 22, November, 1878 of Popular Literature and Science
TankHughes commented on the word algebraic
Algebraic! https://youtu.be/vpG1nR0p0OE
October 8, 2015
hernesheir commented on the word algebraic
See Diophantus.
March 22, 2011