@article { author = {Xarez, Isabel A. and Xarez, Joao J.}, title = {Product preservation and stable units for reflections into idempotent subvarieties}, journal = {Categories and General Algebraic Structures with Applications}, volume = {13}, number = {1}, pages = {1-22}, year = {2020}, publisher = {Shahid Beheshti University}, issn = {2345-5853}, eissn = {2345-5861}, doi = {10.29252/cgasa.13.1.1}, 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}, url = {https://cgasa.sbu.ac.ir/article_87414.html}, eprint = {https://cgasa.sbu.ac.ir/article_87414_21aaa0f023a24966934d960fd660049a.pdf} }