Triangular representations of splitting rings
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- by K. R. Goodearl PDF
- Trans. Amer. Math. Soc. 185 (1973), 271-285 Request permission
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.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 185 (1973), 271-285
- MSC: Primary 16A64
- DOI: https://doi.org/10.1090/S0002-9947-1973-0325697-4
- MathSciNet review: 0325697