Let \(h=\prod _{i=1}^{t}p_i^{s_i}\) be its decomposition into a product of powers of distinct primes, and \(\mathbb {Z}_{h}\) be the residue class ring modulo h. Let \(1\le r\le \min \{m,n\}\) and \(\mathbb {Z}_{h}^{m\times n}\) be the set of all \(m\times n\) matrices over \(\mathbb {Z}_{h}\). The generalized bilinear forms graph over \(\mathbb {Z}_{h}\), denoted by \(\hbox {Bil}_r\left( \mathbb {Z}_{h}^{m\times n}\right) \), has the vertex set \(\mathbb {Z}_{h}^{m\times n}\), and two distinct vertices A and B are adjacent if the inner rank of \(A-B\) is less than or equal to r. In this paper, we determine the clique number and geometric structures of maximum cliques of \(\hbox {Bil}_r\left( \mathbb {Z}_{h}^{m\times n}\right) \). As a result, the Erdős-Ko-Rado theorem for \(\mathbb {Z}_h^{m\times n}\) is obtained.

设\(h=\prod _{i=1}^{t}p_i^{s_i}\)是它分解成不同质数的幂的乘积，并且\(\mathbb {Z}_{h}\)是余数类环模h。设\(1\le r\le \min \{m,n\}\)和\(\mathbb {Z}_{h}^{m\times n}\)是所有\(m\次 n\)矩阵在\(\mathbb {Z}_{h}\) 上。在\(\mathbb {Z}_{h}\) 上的广义双线性形式图，表示为\(\hbox {Bil}_r\left( \mathbb {Z}_{h}^{m\times n}\ right) \)，具有顶点集\(\mathbb {Z}_{h}^{m\times n}\)，以及两个不同的顶点A和B如果\(AB\)的内部秩小于或等于r ，则相邻。在本文中，我们确定了\(\hbox {Bil}_r\left( \mathbb {Z}_{h}^{m\times n}\right) \)的最大团的团数和几何结构。结果，得到了\(\mathbb {Z}_h^{m\times n}\)的 Erdős-Ko-Rado 定理。