A splitting theorem for algebras over commutative von Neumann regular rings
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- by William C. Brown PDF
- Proc. Amer. Math. Soc. 36 (1972), 369-374 Request permission
Abstract:
Let R be a commutative von Neumann ring. Let A be an R-algebra which is finitely generated as an R-module and has $A/N$ separable over R. Here N is the Jacobson radical of A. Then it is shown that there exists an R-separable subalgebra S of A such that $S + N = A$ and $S \cap N = 0$. Further it is shown that if T is another R-separable subalgebra of A for which $T + N = A$ and $T \cap N = 0$, then there exists an element $n \in N$ such that $(1 - n)S{(1 - n)^{ - 1}} = T$. This result is then used to determine the structure of all strong inertial coefficient rings.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 369-374
- MSC: Primary 16A16; Secondary 16A56
- DOI: https://doi.org/10.1090/S0002-9939-1972-0314887-7
- MathSciNet review: 0314887