On the Dimension of Modules and Algebras, X: A Right Hereditary Ring which is not left Hereditary

Irving Kaplansky
1958 Nagoya mathematical journal  
A ringRis said to be right (left) hereditary if every right (left) ideal inRis projective, that is, a direct summand of a freeR-module. Cartan and Eilenberg [3, p. 15] ask whether there exists a right hereditary ring which is not left hereditary. The answer: yes.
doi:10.1017/s0027763000023527 fatcat:5fs2jk3yqrf7rk5i6ujr4xjeie