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1.4 (1965)

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Does there exist a ring without zero divisors which is not embeddable in a skew field, while the multiplicative semigroup of its non-zero elements is embeddable in a group?

Contributor: L. A. Bokut’

Progress

Yes, such groups do exist (L. A. Bokut’, Soviet Math. Dokl., 8 (1967), 901–904; A. Bowtell, J. Algebra, 7 (1967), 126–139; A. Klein, J. Algebra, 7 (1967), 100–125).

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