TITLE: When people say "an algebra" do they always mean "an algebra over a field"?
QUESTION [19 upvotes]: I don't have much experience with abstract algebra. I'm only versed in linear algebra and vector spaces, and have had a tiny introduction to algebras over fields. 
However, this question is a purely terminological one: When people say "an algebra" do they always mean "an algebra over a field"?
If not, what other things can it refer to?

REPLY [4 votes]: It really depends on the context: most of the time it's used for algebras over rings and fields. Sometimes it is used in the most general context of universal algebra as a generic word to talk about a model for an algebraic theory: for example, groups are algebras for the (syntactic) theory of groups.