%0 Journal Article %T Product preservation and stable units for reflections into idempotent subvarieties %J Categories and General Algebraic Structures with Applications %I Shahid Beheshti University %Z 2345-5853 %A Xarez, Isabel A. %A Xarez, Joao J. %D 2020 %\ 07/01/2020 %V 13 %N 1 %P 1-22 %! Product preservation and stable units for reflections into idempotent subvarieties %K Semi-left-exactness %K stable units %K simple reflection %K preservation of finite products %K varieties of universal algebras %K idempotent %R 10.29252/cgasa.13.1.1 %X We 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. %U https://cgasa.sbu.ac.ir/article_87414_21aaa0f023a24966934d960fd660049a.pdf