紧左拓扑左半环的公共幂等元
Common idempotents in compact left topological left semirings
摘要：
拓扑代数的一个经典结果是：任何紧左拓扑半群都有幂等元。我们改进这表明，任何紧凑的左拓扑左半环有一个共同的，即加法和乘法同时，幂等。作为应用，我们部分回答了与自然数上超滤子的代数性质有关的一个问题。最后，我们观察到，类似的论点建立在更一般的，非结合的泛代数的公共幂等元的存在。
英文摘要：
A classical result of topological algebra states that any compact left topological semigroup has an idempotent. We refine this by showing that any compact left topological left semiring has a common, i.e. additive and multiplicative simultaneously, idempotent. As an application, we partially answer a question related to algebraic properties of ultrafilters over natural numbers. Finally, we observe that similar arguments establish the existence of common idempotents in much more general, non-associative universal algebras.
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