Give an example of a commutative ring without zero divisors that is not an integral domain....

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Give an example of a commutative ring without zero divisors that is not an integral domain. If there is no such example, then state so. Give an example of a field that is not an integral domain. If there is no such example, then state so. Prove or disprove: The ring Zg, , > is isomorphic to < Z3 × Z3, 0, Given a ring A = ring B = B, +, A, +, > with underlying set A = {m+n√-2: m, n € Z}, and a with underlying set B = {m+n√-3: m, n € Z}. Show that the mapping 0 A A B defined by 0(m+n√-2) = m + n√ is one-to-one and onto. Show that the mapping is not a ring isomorphism. Give an example of a commutative ring without zero divisors that is not an integral domain. If there is no such example, then state so. Give an example of a field that is not an integral domain. If there is no such example, then state so. Prove or disprove: The ring Zg, , > is isomorphic to < Z3 × Z3, 0, Given a ring A = ring B = B, +, A, +, > with underlying set A = {m+n√-2: m, n € Z}, and a with underlying set B = {m+n√-3: m, n € Z}. Show that the mapping 0 A A B defined by 0(m+n√-2) = m + n√ is one-to-one and onto. Show that the mapping is not a ring isomorphism.