%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
%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 http://cgasa.sbu.ac.ir/article_87414_21aaa0f023a24966934d960fd660049a.pdf