There exists an element e belonging to G, such that a * e = e * a = a for all a belonging to G. (Existence of identity, where e is called the identity in G). This study guide is intended to help students who are beginning to learn about abstract algebra. the branch of mathematics that deals with the extension of algebraic concepts usually associated with the real number system to other, more general systems. The second book is more advanced and includes a nice treatment of Conway's own surreal numbers.

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