Abstract We define the notion of D-set in an arbitrary semigroup, and with some mild restrictions we establish its dynamical and combinatorial characterizations. Assuming a weak form of cancellation in semigroups we have shown that the Cartesian product of finitely many D-sets is a D-set. A similar partial result has been proved for Cartesian product of infinitely many D-sets. Finally, in a commutative semigroup we deduce that D-sets (with respect to a Folner net) are C-sets.

中文翻译：

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任意半群中的 D 集

摘要 我们在任意半群中定义了 D-set 的概念，并在一些温和的限制下建立了它的动力学和组合特征。假设半群中存在弱对消形式，我们已经证明有限多个 D 集的笛卡尔积是 D 集。对于无穷多个 D 集的笛卡尔积，已经证明了类似的部分结果。最后，在交换半群中，我们推导出 D 集（相对于 Folner 网络）是 C 集。