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4 suppose g is an associative closed algebraic structure with...

Question: 4 suppose g is an associative closed algebraic structure with...

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4. Suppose G is an associative, closed algebraic structure with an identity element e, and such that for every a E G there is an element b E G such that ab = e. Prove that G is thus a group. (ie, show that a one-sided inverse property is just as good as the two-sided inverse property which is conventionally used in the definition of a group.)

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