Question: 1 . Let R be a commutative ring with and identity 1 R and 1 R 6 = 0 R . The ideal { 0

1. Let R be a commutative ring with and identity 1R and 1R 6=0R. The ideal {0R} of R which consists only of 0R is called the zero ideal. An ideal I of R with I 6={0R} is called a nonzero ideal. Assume that every nonzero ideal of R equals R. Show that R is a field. (15).

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