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A Ring with Left Identities anb Right Inverses Is a Skew Field

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It is well known that a semigroup in which every element has a left identity and right inverses need not be a group. In this note we prove that if the semigroup is the multiplicative semigroup of a ring, then it is a group. In fact, we have the following theorem.(本文共计1页)......[继续阅读本文]

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