Journal or Book Title
Rocky Mountain Journal of Mathematics
A (left) centralizer for an associative ring R is an additive map satisfying T(xy) = T(x)y for all x, y in R. A (left) Jordan centralizer for an associative ring R is an additive map satisfying T(xy+yx) = T(x)y + T(y)x for all x, y in R. We characterize rings with a Jordan centralizer T. Such rings have a T invariant ideal I, T is a centralizer on R/I, and I is the union of an ascending chain of nilpotent ideals. Our work requires 2-torsion free. This result has applications to (right) centralizers, (two-sided) centralizers, and generalized derivations.
Rocky Mountain Mathematics Consortium
Hentzel, Irvin R. and El-Sayiad, M.S. Tammam, "Left centralizers on rings that are not semiprime" (2011). Mathematics Publications. 129.