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Sudhanshu Ranjan posted an Question
August 16, 2020 • 03:43 am 30 points
  • CSIR NET
  • Mathematical Sciences

Let r be the ring of all continuous function from [o,1] into the real field. show that m = { f | f(0)= 0 } is maximal ideal of r. but m is not maximal ideal if

Let R be the ring of all continuous function from [O,1] into the real field. Show that M = { f | f(0)= 0 } is maximal ideal of R. But M is not maximal ideal if real field is replaced by Integers

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  • Shashi ranjan sinha best-answer

    Suppose real field is replaced by Integers. then the quoteint ring, being isomorphic to Z, is integral domain but not a field. As a result M is just a prime ideal but not maximal ideal

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