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In this paper, we determine the structure of nonlocal commutative rings with $p^6$ zero-divisors and characterize the structure of nonlocal commutative rings with $p^7$ zero-divisors. Also, the structure and classification up to isomorphism all commutative rings with ${p_1}^{k_1}\ldots {p_n}^{k_n}$ zero-divisors, where $n$ is a positive integer, ${p_i}^,s$ are distinct prime number and $1\leq k_i\leq 4$, are determined.
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