#TITLE_ALTERNATIVE# - NURCAHYANI (NIM : 10106042); Pembimbing Tugas Akhir : Prof. Dr. Irawati, ELIH
Let R be a commutative ring with identity 1 = 0. We say that a ring is a chained ring if either x j y or y j x for all x; y 2 R. The set of the zero-divisors of a ring is Z(R), and Nil(R) its ideal of nilpotent elements. The zero-divisor graph of R is T(R) = Z(R) n (0), with distinct vertices x and y adjacent if and only if xy = 0. In this manuscript, we show that the diameter of the zero-divisor graph of a chained ring is diam (T(R)) < 2. The diameter of the zero-divisor graph of a ring such that the prime ideals of R contained in Z(R) are linearly ordered is 2.