On the Structure of Commutative Rings with ${\bf {p_1}^{k_1}\cdots {p_n}^{k_n} Zero Divisors II

Mahmood Behboodi, Reza Beyranvand

Abstract

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.

Keywords

Finite ring, Zero-divisor, Local ring

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