A walk through my work with J. Fountain on classes of (one sided) abundant semigroups

In this talk we will present some of the results obtained with J. Fountain. Special attention will be given to the discussion of the structure of various classes of proper (one sided) abundant semigroups as well as to the existence of proper covers. List of publications with J. Fountain: (1990) The Szendrei expansion of a semigroup, Mathematika 37, 251-260. (1992) Left proper E-dense monoids, Journal of Pure and Applied Algebra 80, 1-27. (1993) Proper left type-A monoids revisited, Glasgow Mathematical Journal 35, 293-306. (1994) Proper left type-A covers, Portugaliae Mathematica 51(2), 305-319. (1999) A Munn type representation for a class of E-semiadequate semigroups (with V. Gould), Journal of Algebra 218, 693-714. (1999) Enlargements, semiabundancy and unipotent monoids (with V. Gould), Communications in Algebra 27(2), 595-614. (2000) Primitive inverse congruences on categorical semigroups, Proceedings of the Edinburgh Mathematical Society 43, 395-413. (2006) Finite abundant semigroups in which the idempotents form a subsemigroup, Journal of Algebra 295, 303-313. (2006) Proper covers of ample monoids, Proceedings of the Edinburgh Mathematical Society 49, 277-289.