There's a mathematical object called an "algebra" (e.g. an algebra over a ring), but why does this particular object have such an "important" name (which makes it sound like the most important concept in this huge area, abstract algebra), whereas the names of other important algebraic structures such as magmas, groups, rings, lattices and modules sound less important. I know some universal algebra and category theory, so I understand that "algebras" have many kin objects. But I can't understand why somebody decided to call these particular objects "algebras", although there seem to be many other good candidates for this grand name.
Similarly, there are objects called "numbers" in number theory, "sets" in set theory, "categories" in category theory, and "topologies" in topology. However, in other areas, for example analysis, geometry and even mathematics, there is no object called an "analysis", a "geometry" or a "mathematics". Is it because there's no fundamental object in these areas which have unsurpassable importance over others? If there are any central objects in these areas which should be named by their significance, in the same way as the objects "category", "topology", and "set" in their respective areas, could you tell me them?