Title of article :
Product preservation and stable units for reflections into idempotent subvarieties
Author/Authors :
Xarez, Isabel A. Department of Mathematics - University of Aveiro, Portugal , Xarez , Joao J. Center for Research and Development in Mathematics and Applications - Department of Mathematics - University of Aveiro, Portugal.
Abstract :
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
Keywords :
Semi-left-exactness , stable units , simple reflection , preservation of finite products , varieties of universal algebras , idempotent
Journal title :
Categories and General Algebraic Structures with Applications
