Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585313120200701Product preservation and stable units for reflections into idempotent subvarieties1228741410.29252/cgasa.13.1.1ENIsabel A. XarezDepartment of Mathematics, University of Aveiro, Portugal.Joao J. XarezCIDMA - Center for Research and Development in Mathematics and Applications,
Department of Mathematics, University of Aveiro, Portugal.0000-0001-8909-2842Journal Article20190117We give a necessary and sufficient condition for the preservation of finite products by a reflection of a variety of universal algebras into an idempotent subvariety. It is also shown that simple and semi-left-exact reflections into subvarieties of universal algebras are the same. It then follows that a reflection of a variety of universal algebras into an idempotent subvariety has stable units if and only if it is simple and the above-mentioned condition holds.https://cgasa.sbu.ac.ir/article_87414_21aaa0f023a24966934d960fd660049a.pdf