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Ends of semigroups. (English) Zbl 1396.20064

Summary: We define the notion of the partial order of ends of the Cayley graph of a semigroup. We prove that the structure of the ends of a semigroup is invariant under change of finite generating set and at the same time is inherited by subsemigroups and extensions of finite Rees index. We prove an analogue of Hopf’s Theorem, stating that an infinite group has 1, 2 or infinitely many ends, for left cancellative semigroups and that the cardinality of the set of ends is invariant in subsemigroups and extension of finite Green index in left cancellative semigroups.

MSC:

20M05 Free semigroups, generators and relations, word problems
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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