Suppose that S is a semigroup with left identity and left inverse, prove that it is a group. Well, since it is a semigroup, S already has the associativity property, but how do I show it has the right id and right inverse? Thank you
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Originally Posted by tttcomrader Suppose that S is a semigroup with left identity and left inverse, prove that it is a group. Well, since it is a semigroup, S already has the associativity property, but how do I show it has the right id and right inverse? Thank you let be a left identity and so also thus so is also a right inverse of finally we have: i.e. is a right identity as well. Q.E.D.
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