Definition of an Algebraic Objects How did the definition of Algebraic objects like group, ring and field come up? When groups were first introduced, were they given the 4 axioms as we give now. And what made Mathematicians to think of something like this.

With respect to the introduction of fields, Erich Reck in his "Dedekind's Contributions to the Foundations of Mathematics", cites Dedekind as being the first to introduce this concept into mathematics, in the context of his work in algebraic number theory. Reck's article goes into some detail about Dedekind's other contributions to mathematics that seem like they may be of interest, for example, his work on lattices.
