Stokes, Tim E.2019-12-022015-01-012019-12-022015Stokes, T. E. (2015). Domain and range operations in semigroups and rings. Communications in Algebra, 43(9), 3979–4007. https://doi.org/10.1080/00927872.2014.9375330092-7872https://hdl.handle.net/10289/13246A D-semigroup S is a semigroup equipped with an operation D satisfying laws asserting that for a ∈ S, D(a) is the smallest e in some set of idempotents U ⊆ S for which ea = a. D-semigroups correspond to left-reduced U-semiabundant semigroups. The basic properties and many examples of D-semigroups are given. Also considered are D-rings, whose multiplicative semigroup is a D-semigroup. Rickart *-rings provide important examples, and the most general D-rings for which the elements of the form D(a) constitute a lattice under the same meet and join operations as for Rickart *-rings are described.application/pdfenThis is an author’s accepted version of an article published in the journal: Communications in Algebra. © 2015 Taylor & Francis Group.Science & TechnologyPhysical SciencesMathematicsRickart *-ringU-semiabundant semigroupU-semiadequate semigroupRESTRICTION SEMIGROUPSABUNDANT SEMIGROUPSCATEGORIESALGEBRASJournal Article10.1080/00927872.2014.9375331532-4125