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Sudhanshu Ranjan posted an Question
August 22, 2020 • 05:45 am 30 points
  • CSIR NET
  • Mathematical Sciences

What is the form of an ideal generated by an element"a" of a ring r?

what is the form of an ideal generated by an element"a" of a ring R?

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  • Shashi ranjan sinha best-answer

    However, there is no explicit description of the ideal generated by a if R doesn't have unity

  • Shashi ranjan sinha Best Answer

    Suppose R has unity. Then, 1) The left ideal generated by a is of the form Ra = {ra : r € R }. 2) The right ideal generated by a is of the form, aR ={ar :r€R} 3) The both sided ideal is given by RaR , consisting of all finite sum of the terms of the form "ras", where r,s belongs to R In case R is CRU, all these three ideals are equal

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