Abstract
We show that any Bruck-Reilly extension of an inverse monoid is an HNN extension of a certain inverse monoid. We also discuss several decision problems. The word problem for a Bruck-Reilly extension of an inverse monoid is solvable under a reasonable condition. On the other hand, many algebraic properties for Bruck-Reilly extensions of inverse monoids are undecidable. Key words : Inverse monoids, Bruck-Reilly extensions, HNN extensions, Decision problems. AMS Mathematics Subject Classification: 20M18, 20M05
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