Solution to a problem by FitzGerald

@article{Hemelaer2020SolutionTA,
  title={Solution to a problem by FitzGerald},
  author={Jens Hemelaer and Morgan Rogers},
  journal={arXiv: Rings and Algebras},
  year={2020}
}
FitzGerald identified four conditions (RI), (UR), (RI*) and (UR*) that are necessarily satisfied by an algebra, if its monoid of endomorphisms has commuting idempotents. We show that these conditions are not sufficient, by giving an example of an algebra satisfying the four properties, such that its monoid of endomorphisms does not have commuting idempotents. This settles a problem presented by Fitzgerald at the Conference and Workshop on General Algebra and Its Applications in 2013 and more… Expand

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