On the nature and number of isomorphism classes of the minimal ring extensions of a finite commutative ring

DOI10.1080/00927872.2020.1748193zbMath1457.13017OpenAlexW3015566090MaRDI QIDQ5131749

David E. Dobbs

Publication date: 9 November 2020

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927872.2020.1748193

zbMATH Keywords

finite fieldlocal ringintegralcommutative ringdirect productfinite ringinertminimal ring extensionidealizationdecomposedartinian ringcrucial maximal idealramified

Mathematics Subject Classification ID

Extension theory of commutative rings (13B02) Integral dependence in commutative rings; going up, going down (13B21)

Related Items (4)

Certain towers of ramified minimal ring extensions of commutative rings, II ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Where some inert minimal ring extensions of a commutative ring come from. II

Cites Work

• Minimal integral ring extensions
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• Cyclic and Negacyclic Codes Over Finite Chain Rings
• On the Prime Ideals in a Commutative Ring
• Certain towers of ramified minimal ring extensions of commutative rings
• A minimal ring extension of a large finite local prime ring is probably ramified
• Characterizing finite fields via minimal ring extensions
• On the FIP Property for Extensions of Commutative Rings
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