تعریف عضو وارون

تعریف عضو وارون چپ و راست روشن است.

Definition. Let be a semigroup with identity e. Let a E S. If there exists an element b in S such that ab = e = ba,

then b is called the inverse of a, and a is said to be invertible.

Definition. A nonempty set G with a binary operation . on G is called a group jfthefollowing axioms hold:

(i) a(bc) = (ab)cfor all a,b,c E G. (ii) There exists e E G such that ea = afor all a E G. (iii) For every a E G there exists a' G such that a'a = e.

If the binary operation in a group (G,•) is commutative — that is. ab = ba for all a,b E G — then the group is called commutative or abelian.

تا اینجا: یک مجموعه که ضرب شرکت پذیر، عضو خنثی و وارون گروه. اگر ضرب جابجایی گروه آبلی

Let (S,') be a semigroup. Since- is associative, Theorem 4.2 (Chapter 1) holds here, and therefore there is a unique product of any given elements E S, in that order, that are written For any positive integer n we define, as before, a = aa...a (n-fold product), which is called the nih power of a.