Finite Presentability of Bruck–Reilly Extensions of Semilattices

Abstract

Let Y be a semilattice with an identity element, and let θ be an endomorphism of Y. We prove that if the Bruck–Reilly extension BR(Y, θ) is finitely presented, then Y is finite.

Key Words:

• Generators
• Monoid
• Presentation
• Semilattice

Mathematics Subject Classification:

• 20M05
• 20M10
• 20M14

ACKNOWLEDGMENT

Carvalho acknowledges the financial support of the Fundação para a Ciência e a Tecnologia (Grant no. SFRH/BD/8113/2002).

Notes

Communicated by V. Gould.