The endomorphism ring of an Artinian module whose homogeneous length is finite
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- by Rainer Schulz PDF
- Proc. Amer. Math. Soc. 86 (1982), 209-210 Request permission
Abstract:
Smalø[2] showed that the index of nilpotency of the endomorphism ring of a module ${M_R}$ of finite length is bounded by the number $\max \left \{ {{n_A}|{A_R}\;{\text {simple}}} \right \}$, where ${n_A}$ denotes the number of times ${A_R}$ occurs as a factor in a composition chain of ${M_R}$. We give another proof of Smalø’s theorem which leads to an analogous result for artinian modules whose homogeneous length is finite.References
- Joe W. Fisher, Nil subrings of endomorphism rings of modules, Proc. Amer. Math. Soc. 34 (1972), 75–78. MR 292878, DOI 10.1090/S0002-9939-1972-0292878-2
- Sverre O. Smalø, A limit on the Loewy length of the endomorphism ring of a module of finite length, Proc. Amer. Math. Soc. 81 (1981), no. 2, 164–166. MR 593447, DOI 10.1090/S0002-9939-1981-0593447-2
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 209-210
- MSC: Primary 16A65; Secondary 16A22
- DOI: https://doi.org/10.1090/S0002-9939-1982-0667274-2
- MathSciNet review: 667274