The Loewy series of an FCP (distributive) ring extension

zbMath1471.13021arXiv1909.13729MaRDI QIDQ5004255

Gabriel Picavet, Martine Picavet-L'Hermitte

Publication date: 30 July 2021

Full work available at URL: https://arxiv.org/abs/1909.13729

zbMATH Keywords

atomminimal extensionGalois extensionBoolean latticedistributive latticesocleLoewy seriesFCP extensionFIPsupport of a module

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Integral closure of commutative rings and ideals (13B22) Structure and representation theory of distributive lattices (06D05) Extension theory of commutative rings (13B02) Integral dependence in commutative rings; going up, going down (13B21) Structure theory of Boolean algebras (06E05) Rings of fractions and localization for commutative rings (13B30)

Related Items

Catenarian FCP ring extensions ⋮ Splitting ring extensions ⋮ Unnamed Item

Cites Work

• New results about normal pairs of rings with zero-divisors
• Manis valuations and Prüfer extensions. I: A new chapter in commutative algebra
• Pointwise minimal extensions
• A note on a class of extensions
• Characterizing the ring extensions that satisfy FIP or FCP
• Catenarian FCP ring extensions
• When an extension of Nagata rings has only finitely many intermediate rings, each of those is a Nagata ring
• Homomorphismes minimaux d'anneaux
• MODULES WITH FINITELY MANY SUBMODULES
• Quasi-Prüfer Extensions of Rings
• Boolean FIP ring extensions
• Ring extensions of length two
• Prüfer and Morita Hulls of FCP Extensions
• Transfer Results for the FIP and FCP Properties of Ring Extensions
• On the existence of exceptional field extensions
• On the FIP Property for Extensions of Commutative Rings
• On seminormality
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item