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let x be an element of a commutative ring  R which has an inverse x^.pdf

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let x be an element of a commutative ring R which has an inverse x^-1 ,let y be another element of R such that y^2=0. prove that x+y has an inverse in R? Solution as y^2=0 we don\'t have any inverse of y as y=0 but for the case of x+y we have as x have an exsisting inverse we have x is not equal to 0. so x+y can\'t be zero as x is never zero. so for an inverse to exsist we have to have only one necessar condition i.e it shouldn\'t be zero which is satisified. so x+y has an inverse in R.

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let x be an element of a commutative ring R which has an inverse x^-1 ,let y be another element of R such that y^2=0. prove that x+y has an inverse in R? Solution as y^2=0 we don't have any inverse of y as y=0 but for the case of x+y we have as x have an exsisting inverse we have x is not equal to 0. so x+y can't be zero as x is never zero. so for an inverse to exsist we have to have only one necessar condition i.e it shouldn't be zero which is satisified. so x+y has an inverse in R

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let x be an element of a commutative ring  R which has an inverse x^.pdf

  • 1. let x be an element of a commutative ring R which has an inverse x^-1 ,let y be another element of R such that y^2=0. prove that x+y has an inverse in R? Solution as y^2=0 we don't have any inverse of y as y=0 but for the case of x+y we have as x have an exsisting inverse we have x is not equal to 0. so x+y can't be zero as x is never zero. so for an inverse to exsist we have to have only one necessar condition i.e it shouldn't be zero which is satisified. so x+y has an inverse in R