On the coherence and weak dimension of the rings $R\langle x\rangle$ and $R(x)$
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- by Sarah Glaz PDF
- Proc. Amer. Math. Soc. 106 (1989), 579-587 Request permission
Abstract:
Let $R$ be a commutative ring. We first derive necessary and sufficient conditions for the rings $R\left \langle x \right \rangle$ and $R(x)$ to be coherent. Next, for stably coherent rings of finite weak dimension exact relations are found between the weak dimension of $R$ and that of $R\left \langle x \right \rangle$ and $R(x)$. These relations are used to determine necessary and sufficient conditions for $R\left \langle x \right \rangle$ and $R(x)$ to be Von Neumann regular or semihereditary.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 579-587
- MSC: Primary 13F20
- DOI: https://doi.org/10.1090/S0002-9939-1989-0961405-9
- MathSciNet review: 961405