Semigroup Forum ( IF 0.7 ) Pub Date : 2021-08-19 , DOI: 10.1007/s00233-021-10222-w Neil Hindman 1 , Dona Strauss 2
Given a discrete semigroup \((S,\cdot )\), there is a natural operation on the Stone–Čech compactification \(\beta S\) of S which extends the operation of S and makes \((\beta S,\cdot )\) a compact right topological semigroup with S contained in its topological center. If S and T are discrete semigroups, \(p\in \beta S\), and \(q\in \beta T\), then the tensor product \(p\otimes q\) is a member of \(\beta (S\times T)\). It is known that tensor products are both algebraically and topologically rare in \(\beta (S\times T)\). We investigate when the algebraic product of two tensor products is again a tensor product. We get a simple characterization for a large class of semigroups. The characterization is in terms of a notion of cancellation. We investigate where that notion sits among standard cancellation notions.
中文翻译:
张量积的代数积
给定的离散半群\((S,\ CDOT)\) ,上有斯通-切赫紧化自然的操作\(\测试小号\)的小号延伸的操作小号和品牌\((\测试S, \cdot )\)一个紧缩右拓扑半群,其拓扑中心包含S。如果S和T是离散半群\(p\in \beta S\)和\(q\in \beta T\),那么张量积 \(p\otimes q\)是\(\测试版 (S\times T)\)。众所周知,张量积在代数和拓扑上都是罕见的\(\beta (S\times T)\)。我们调查两个张量积的代数积何时再次成为张量积。我们得到了一大类半群的简单刻画。表征是根据取消的概念。我们调查该概念在标准取消概念中的位置。