A noetherian ring R is Krull symmetric if for every pair of ideals \(T\subseteq S\) of R the right and left Krull dimensions of S/T are equal. A module M is K-homogeneous if all non-zero submodules of M have the same Krull dimension. In general, the sum of two homogeneous left ideals of the same Krull dimension need not be homogeneous. However, if R is a Krull symmetric noetherian ring such that the associated primes of R are minimal primes, then the sum of homogeneous left ideals with the same Krull dimension is homogeneous. In this case, for any ordinal \(\alpha\), the ring contains a unique maximal homogeneous ideal \(H_{\alpha}\) of Krull dimension \(\alpha\). Only finitely many \(H_{\alpha}\) are non-zero and their direct sum is a faithful ideal of R. The ring R has an artinian classical quotient ring if and only if this non-zero ideal contains a non-zero-divisor. Finally, the previous result is used to obtain another proof of a theorem due to Warfield concerning decompositions of rings.