Stable event structures, and their duality with prime algebraic domains, represent a landmark of concurrency theory, since they provide a neat characterisation of causality in computations. As such, they have been used for defining the concurrent semantics of many formalisms, from Petri nets to (linear) graph rewriting systems.

Stability however is restrictive for formalisms with “fusion”, where a computational step may merge parts of the state. This happens e.g. for graph rewriting systems with non-linear rules, which are used to cover some relevant applications (such as the graphical encoding of calculi with name passing).

Guided by the need of giving semantics to such formalisms, we leave aside stability and characterise a class of domains, referred to as weak prime domains, naturally generalising prime algebraic domains. We then identify a corresponding class of event structures, that we call connected event structures, via a duality result formalised as an equivalence of categories.

稳定的事件结构及其与素数代数域的对偶性代表了并发理论的里程碑，因为它们提供了计算中因果关系的简洁表征。因此，它们已被用于定义许多形式主义的并发语义，从 Petri 网到（线性）图重写系统。

然而，稳定性对于具有“融合”的形式主义是有限制的，其中计算步骤可能会合并部分状态。这发生在例如具有非线性规则的图重写系统中，这些系统用于覆盖一些相关应用（例如具有名称传递的演算的图形编码）。

在为这种形式主义提供语义的需要的指导下，我们抛开稳定性并刻画一类域，称为弱素域，自然地概括素代数域。然后，我们通过形式化为类别等价的对偶结果识别出相应的事件结构类，我们称之为连接事件结构。