Generators and Relations for Subsemigroups via Boundaries in Cayley Graphs

نویسندگان

  • R. Gray
  • N. Ruškuc
چکیده

Given a finitely generated semigroup S and subsemigroup T of S we define the notion of the boundary of T in S which, intuitively, describes the position of T inside the left and right Cayley graphs of S. We prove that if S is finitely generated and T has a finite boundary in S then T is finitely generated. We also prove that if S is finitely presented and T has a finite boundary in S then T is finitely presented. Several corollaries and examples are given.

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تاریخ انتشار 2011