Tài liệu Elementary Abstract Algebra docx

[...]... them One of the problems is stating precisely what is meant by \inserting the parentheses in a legal manner" The interested reader can nd a proof in most introductory abstract algebra books See for example Chapter 1.4 of the book Basic Algebra I 9] by Nathan Jacobson Remark From now on, unless stated to the contrary, we will assume the Generalized Associative Law That is, we will place parentheses in...3 a set S , we write a b instead of (a b) This is called in x notation In practice, we abbreviate even more just as we use ab instead of a b or a b in high school algebra, we will often use ab instead of a b for a generic binary operation Notation We denote the natural numbers, the integers, the rational numbers, and the real numbers by the symbols N , Z, Q , and