Commutativity of rings with abelian or solvable units

Nicholson, W. K.; Springer, H. J.

doi:10.1090/S0002-9939-1976-0399180-2

Commutativity of rings with abelian or solvable units
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by W. K. Nicholson and H. J. Springer

Proc. Amer. Math. Soc. 56 (1976), 59-62

DOI: https://doi.org/10.1090/S0002-9939-1976-0399180-2

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Abstract:

A ring is called left suitable if idempotents can be lifted modulo every left ideal. These rings include all regular and all semiperfect rings. A left suitable ring with abelian group of units is commutative if it is either semiprime or $2$-torsion-free. A left suitable ring with zero Jacobson radical and solvable group of units is commutative if it is $6$-torsion-free.

References

Loo-Keng Hua, On the multiplicative group of a field, Acad. Sinica Science Record 3 (1950), 1–6 (English, with Chinese summary). MR 0039707
Charles Lanski, Subgroups and conjugates in semi-prime rings, Math. Ann. 192 (1971), 313–327. MR 286840, DOI 10.1007/BF02075359
Charles Lanski, Some remarks on rings with solvable units, Ring theory (Proc. Conf., Park City, Utah, 1971) Academic Press, New York, 1972, pp. 235–240. MR 0342565
W. K. Nicholson, Semiperfect rings with abelian group of units, Pacific J. Math. 49 (1973), 191–198. MR 332860

Bibliographic Information

Journal: Proc. Amer. Math. Soc. 56 (1976), 59-62
DOI: https://doi.org/10.1090/S0002-9939-1976-0399180-2
MathSciNet review: 0399180