Simple graded rings. (English) Zbl 0786.16020
Necessary and sufficient conditions are given for a ring graded by a hypercentral group to be simple. For example, it is proved that such a ring \(R\) is simple if and only if it is graded simple and \(Z(R)\) is a field.
Reviewer: S.Raianu (Bucureşti)
MSC:
| 16W50 | Graded rings and modules (associative rings and algebras) |
| 16D60 | Simple and semisimple modules, primitive rings and ideals in associative algebras |
Keywords:
graded simple ringsReferences:
| [1] | Bell Allan D., J. Algebra 105 pp 76– (1987) · Zbl 0607.16013 · doi:10.1016/0021-8693(87)90181-5 |
| [2] | Cohen M., Trans. Amer. Math. Soc 282 (1) pp 237– (1984) · doi:10.1090/S0002-9947-1984-0728711-4 |
| [3] | Handelman D., Houston J. Math 4 (1) pp 175– (1978) |
| [4] | McLain D.H., Proc Glasgow Math. Assoc 3 (1) pp 38– (1956) · Zbl 0072.25702 · doi:10.1017/S2040618500033414 |
| [5] | Nastasescu C., Graded Ring Theory (1982) |
| [6] | Paasman D.S., The algebraic structure of group rings (1977) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
