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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Triangular representations of splitting rings


Author: K. R. Goodearl
Journal: Trans. Amer. Math. Soc. 185 (1973), 271-285
MSC: Primary 16A64
MathSciNet review: 0325697
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Abstract: The term ``splitting ring'' refers to a nonsingular ring R such that for any right R-module M, the singular submodule of M is a direct summand of M. If R has zero socle, then R is shown to be isomorphic to a formal triangular matrix ring $ \left( {\begin{array}{*{20}{c}} A & 0 \\ B & C \\ \end{array} } \right)$, where A is a semiprime ring, C is a left and right artinian ring, and $ _C{B_A}$ is a bimodule. Also, necessary and sufficient conditions are found for such a formal triangular matrix ring to be a splitting ring.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0325697-4
PII: S 0002-9947(1973)0325697-4
Keywords: Nonsingular ring, singular submodule, splitting properties, splitting ring
Article copyright: © Copyright 1973 American Mathematical Society