In mathematics, a Gelfand ring is an associative ringR 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.[1]
In the commutative case, Gelfand rings can also be characterized as the rings such that, for every a and b summing to 1, there exists r and s such that
gelfand, ring, mathematics, associative, ring, with, identity, such, that, distinct, right, ideals, then, there, elements, such, that, mulvey, 1979, introduced, them, rings, which, could, prove, generalization, gelfand, duality, named, them, after, israel, gel. 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 1 In the commutative case Gelfand rings can also be characterized as the rings such that for every a and b summing to 1 there exists r and s such that 1 r a 1 s b 0 displaystyle 1 ra 1 sb 0 Moreover their prime spectrum deformation retracts onto the maximal spectrum 2 3 References Edit 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 Contessa Maria 1982 01 01 On pm rings Communications in Algebra 10 1 93 108 doi 10 1080 00927878208822703 ISSN 0092 7872 algebraic geometry When does the prime spectrum deformation retract into the maximal spectrum Mathematics Stack Exchange Retrieved 2020 10 16 This abstract algebra related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Gelfand ring amp oldid 1032051756, wikipedia, wiki, book, books, library,
