Biderivations on trivial extension algebras

Document Type : Original Article


1 Department of Mathematics, Faculty of Basic Sciences, University of Bo- jnord, P. O. Box 1339, Bojnord, IRAN.

2 Department of Biostatistics, School of Allied Medical Sciences, Shahid Beheshti University of Medical sciences, Tehran, IRAN.



We investigate biderivations, inner biderivations and extremal biderivations on a trivial extensions algebra. Our results are examined for some special trivial extension algebras, such as triangular algebras and certain generalized matrix algebras, renovating some older results. We also study biderivations on a unital algebra with a nontrivial idempotent, extending a variety of results to some more general algebras.