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group ring; s-weakly regular ring
In this note we obtain a necessary and sufficient condition for a ring to be $s$-weakly regular (i) When $R$ is a ring with identity and without divisors of zero (ii) When $R$ is a ring without divisors of zero. Further it is proved in a $s$-weakly regular ring with identity and without units every element is a zero divisor.
[1] Gupta, V.: A generalization of strongly regular rings. Acta. Math. Hungar 43 (1984), No 1-2, 57-61. MR 0731964 | Zbl 0535.16015
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