Abstract
We give an upper bound for the descending Loewy length of the ring S=End(M), where M is a semi-artinian R-module satisfying some extra-conditions.
In case M is of finite length, our main result specializes to the following result, which improves a theorem of Smalø ([3]): The index of nilpotency of Ra(S) is bounded by the number max{lA¦A is a simple R-module occuring in the socle of M}, where lA denotes the number of times the isomorphism type of A occurs as a factor in a composition chain of M.
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Literatur
DISCHINGER, F.: Stark π-reguläre Ringe. Dissertation. Universität München 1977
SCHULZ, R.: The endomorphism ring of an artinian module whose homogeneous length is finite. Proc. Amer. Math. Soc.86, 209–210 (1982)
SMALØ, S.O.: A limit on the Loewy length of the endomorphism ring of a module of finite length. Proc. Amer. Math. Soc.81, 164–166 (1981)
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Schulz, R. Die absteigende Loewy-Länge von Endomorphismenringen. Manuscripta Math 45, 107–113 (1984). https://doi.org/10.1007/BF01169768
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DOI: https://doi.org/10.1007/BF01169768