Unit-regular orthodox semigroups
Glasgow mathematical journal, Tome 25 (1984) no. 2, pp. 229-240

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Unit-regular rings were introduced by Ehrlich [4]. They arose in the search for conditions on a regular ring that are weaker than the ACC, DCC, or finite Goldie dimension, which with von Neumann regularity imply semisimplicity. An account of unit-regular rings, together with a good bibliography, is given by Goodearl [5].
McFadden, R. B. Unit-regular orthodox semigroups. Glasgow mathematical journal, Tome 25 (1984) no. 2, pp. 229-240. doi: 10.1017/S0017089500005656
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