Zariski-Samuel define an unmixed/equidimensional ideal to be one whose associated primes have the same dimension. At other places I have seen definitions saying unmixed=all associated primes have same height equidimensional==all associated primes have same dimension
Are these two definitions equivalent?
One says that an ideal $I$ is unmixed if $I$ has no embedded prime divisors or, in modern language, if the associated prime ideals of $R/I$ are the minimal prime ideals of $I$. However, an ideal $I$ is said to be equidimensional if every minimal prime ideal of $I$ has the same dimension.