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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, MR 0528590

Mathematics Encyclopedia