Arithmetical Rings and Krull Dimension
Abstract
Let $A$ be a commutative arithmetical ring. The ring $A$ has Krull dimension if and only if every factor ring of $A$ is finite-dimensional and does not have idempotent proper essential ideals. The study is supported by Russian Science Foundation (project no. 16-11-10013).
- Publication:
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arXiv e-prints
- Pub Date:
- April 2017
- DOI:
- 10.48550/arXiv.1705.00181
- arXiv:
- arXiv:1705.00181
- Bibcode:
- 2017arXiv170500181T
- Keywords:
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- Mathematics - Rings and Algebras
- E-Print:
- 7 pages