A limit on the Loewy length of the endomorphism ring of a module of finite length
Author: Sverre O. Smalø
Journal: Proc. Amer. Math. Soc. 81 (1981), 164-166
MSC: Primary 16A65; Secondary 16A64
MathSciNet review: 593447
Abstract: Let be a module of finite length over an arbitrary ring . Let be the nonisomorphic simple composition factors of and let denote that occurs times in a composition series for . As a generalization of Schur's lemma we have the following wellknown result: If is nonzero and all the are equal to one then the Loewy length of the endomorphism ring of is one. We will generalize this fact showing that in general the Loewy length of the endomorphism ring of is less than or equal to the maximum of the , .