Contributions to zero-sum problems

A prototype of zero-sum theorems, the well-known theorem of Erdős, Ginzburg and Ziv says that for any positive integer n  , any sequence a1,a2,…,a2n-1a1,a2,…,a2n-1 of 2n-12n-1 integers has a subsequence of n elements whose sum is 0 modulo n  . Appropriate generalizations of the question, especially that for (Z/pZ)d(Z/pZ)d, generated a lot of research and still have challenging open questions. Here we propose a new generalization of the Erdős–Ginzburg–Ziv theorem and prove it in some basic cases.