Abstract
We investigate the uniseriality of uniform injective modules over serial rings. Let R be an arbitrary ring and fix a decomposition, of the identity, 1 = e 1 + e 2 + ⋯ + e n into orthogonal idempotents. For any uniform injective module V R , we prove that there exists e = e i such that, with A = eRe, V R ≅ hom A (Re,Ve). Moreover, Ve is a uniform injective A-module. We also show that if R is Goldie prime serial, then V is uniserial if and only if Ve is uniserial as an A-module.
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© 1997 Springer Science+Business Media New York
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Guerriero, F. (1997). Uniform Modules Over Goldie Prime 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_10
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DOI: https://doi.org/10.1007/978-1-4612-1978-1_10
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7364-6
Online ISBN: 978-1-4612-1978-1
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