We study the direct sum of q-matroids by way of their cyclic flats. Using that the rank function of a q-matroid is fully determined by the cyclic flats and their ranks, we show that the cyclic flats of the direct sum of two q-matroids are exactly all the direct sums of the cyclic flats of the two summands. This simplifies the rank function of the direct sum significantly. A q-matroid is called irreducible if it cannot be written as a (non-trivial) direct sum. We provide a characterization of irreducibility in terms of the cyclic flats and show that every q-matroid can be decomposed into a direct sum of irreducible q-matroids, which are unique up to equivalence.

翻译：本文通过循环平坦结构研究q-拟阵的直和分解。利用q-拟阵的秩函数完全由其循环平坦及其秩决定这一性质，我们证明两个q-拟阵直和的循环平坦恰好等于两个被加项循环平坦的直和，这显著简化了直和的秩函数表达。若一个q-拟阵不能表示为（非平凡）直和形式，则称其为不可约的。我们给出了基于循环平坦的不可约性刻画，并证明每个q-拟阵均可分解为若干不可约q-拟阵的直和，且该分解在等价意义下唯一。