The Connotation of an "Algebra" I am studying some real analysis as we speak, currently on the topic of function spaces. In particular, this section of my book is discussing function algebras. I have heard of other types of algebras, such as $\sigma-$algebras, Kac-Moody algebras, operator algebras etc. 
My question is simple: Intuitively, when I hear "______ algebra", what should I think of? That is, what kind of structure is an algebra- what is the connotation of the word? Is it generally any type of algebraic structure?

In general an algebra means

a structure with one or more binary operations satisfying certain rules, but where those rules didn't get one of the fancy names like "ring" or "field" because they ran out of good words before this particular set of rules were first considered.

Many kinds of algebras belong to a narrower group,

something that is either a vector space or a module over some ring, and which additionally has a binary operation that distributes over the vector/module addition and can -- to some extent -- be thought of as a "multiplication" operation.

But the only way to be sure that what you're looking at belongs to this narrower concept is to look at the definition, so that is not really helpful.
