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Sudhanshu ranjan Asked a Question
August 25, 2020 1:12 ampts 30 pts
  • CSIR NET
  • Mathematical Sciences

Is the quoteint ring of an integral domain still an integral domain?

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  • Shashi ranjan sinha Best Answer
    Example 2 : R =Z and I = 4Z , then R/ I has ( 2+4Z ) as zero divisior and so R/I is not integral domain
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  • Shashi ranjan sinha thankyou
    Example 1 : let R = Z and I ={0} , then R/I is isomorphic to R = Z which is integral domain
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  • Shashi ranjan sinha
    No, it is not necessary that the quoteint ring of ID is still ID... It may or may not be an integral domain
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