Bruck-reilly extensions of quasi-automatic semigroups

  • Yanhui Wang
  • Yuhan Wang
  • Xueming Ren


The interaction of quasi-automatic semigroups and Bruck-Reilly extensions is studied. It is showed that a Bruck-Reilly extension BR(T; theta) of an automatic monoid S is itself quasi-automatic if S is finite; if the mapping theta : S → S sends everything to 1S ; if theta : S → S is the identity mapping; or if S is of finite geometric type and Stheta is finite. Such results are analogues to Andrade, Descalco and Martins’s results for the automatic case.

How to Cite
WANG, Yanhui; WANG, Yuhan; REN, Xueming. Bruck-reilly extensions of quasi-automatic semigroups. Eurasian Bulletin of Mathematics (ISSN: 2687-5632), [S.l.], p. 69-77, may 2018. ISSN 2687-5632. Available at: <>. Date accessed: 27 jan. 2022.