Gelfand ring

In mathematics, a Gelfand ring is an associative ring R with identity such that if I and J are distinct right ideals then there are elements i and j such that iRj=0, i is not in I, and j is not in J. Mulvey (1979) introduced them as rings for which one could prove a generalization of Gelfand duality, and named them after Israel Gelfand.

References

• Mulvey, Christopher J. (1979), "A generalisation of Gelʹfand duality.", J. Algebra 56 (2): 499–505, doi:10.1016/0021-8693(79)90352-1, MR 0528590