{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,19]],"date-time":"2023-02-19T19:07:44Z","timestamp":1676833664823},"reference-count":22,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2003,8]]},"abstract":"<jats:p> We consider universal algebras which are monoids and which have a binary operation we call internalized equality, satisfying some natural conditions. We show that the class of such E-structures has a characterization in terms of a distinguished submonoid which is a semilattice. Some important varieties (and variety-like classes) of E-structures are considered, including E-semilattices (which we represent in terms of topological spaces), E-rings (which we show are equivalent to rings with a generalized interior operation), E-quantales (where internalized equalities on a fixed quantale in which 1 is the largest element are shown to correspond to sublocales of the quantale), and EI-structures (in which an internalized inequality is defined and interacts in a natural way with the equality operation). <\/jats:p>","DOI":"10.1142\/s021819670300147x","type":"journal-article","created":{"date-parts":[[2003,11,21]],"date-time":"2003-11-21T03:49:01Z","timestamp":1069386541000},"page":"463-480","source":"Crossref","is-referenced-by-count":6,"title":["VARIETIES OF EQUALITY STRUCTURES"],"prefix":"10.1142","volume":"13","author":[{"given":"DESMOND","family":"FEARNLEY-SANDER","sequence":"first","affiliation":[{"name":"c\/o School of Mathematics and Physics,  University of Tasmania, Australia"}]},{"given":"TIM","family":"STOKES","sequence":"additional","affiliation":[{"name":"Mathematics and Statistics,  Division of Science and Engineering, Murdoch University, Australia"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129500000189"},{"key":"rf2","doi-asserted-by":"crossref","first-page":"25","DOI":"10.4064\/cm-29-1-25-29","volume":"29","author":"Bloom S. 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