Abstract
Let R be an artinian ring with Jacobson radical J such that J 2 = 0 and R/J is a direct product of matrix rings over finite dimensional division rings. The structure of R is determined, in case every indecomposable right R-module is uniform. Furthermore, all indecomposable right or left modules over such a ring are determined.
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References
V. Dlab and C.M. Ringel, Decomposition of Modules over right uniserial rings, Math. Z. 129 (1972), 207–230.
V. Dlab and C.M. Ringel, The structure of balance rings, Proc. London Math. Soc. (3), 26 (1973), 446–462.
C. Faith, Algebra II, Ring Theory, Grundleheren der Mathematischen Wissenschaften, 19, Springer-Verlag, 1976.
N. Jacobson, Structure of Rings, Second Edition, Colloquium Publications, 37, American Mathematical Society, 1956.
S. Singh, Artinian right serial rings, Proc. Amer. Math. Soc. (to appear).
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© 1997 Springer Science+Business Media New York
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Singh, S. (1997). Indecomposable Modules Over Artinian Right Serial Rings. In: Jain, S.K., Rizvi, S.T. (eds) Advances in Ring Theory. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1978-1_23
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DOI: https://doi.org/10.1007/978-1-4612-1978-1_23
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7364-6
Online ISBN: 978-1-4612-1978-1
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