Algebra

[Pierre Abbat <phma@webjockey.net>]

There are at least four different meanings of "algebra, algebraic" in 
mathematics. I don't think it's right to call them all {aljebra}, so I try to 
come up with terms for them:

1. The basic meaning of "algebra" is manipulation of mekso. What's the word 
for "manipulate"?
2. Abstract algebra, in one sense, is the study of sujgri, piljygri, and 
dilcygri. So <operation> girzu saske. But what's the word for "operation"?
(The other sense is algebra, in the first sense, in fields other than Q, R, 
or C. For instance, one can compute an elliptic curve sum by taking the 
formal derivative of a polynomial in a finite field and get sensible results, 
even though taking a derivative of a function in a finite field makes no 
sense.)
3. An algebra is a vector space with multiplication. {farlaili'i piljygri}?
4. An algebraic number is a number which is a solution to a polynomial 
equation.

Any more suggestions?

phma