The Laskerian Property, Power Series Rings and Noetherian Spectra

DOI10.2307/2042378zbMath0447.13009OpenAlexW4243186705MaRDI QIDQ3892346

Robert Gilmer, William J. Heinzer

Publication date: 1980

Full work available at URL: https://doi.org/10.2307/2042378

zbMATH Keywords

zero divisorsNoetherian ringpower series ringsNoetherian spectrumZD-ringLaskerian ring

Mathematics Subject Classification ID

Commutative Noetherian rings and modules (13E05) Ideals and multiplicative ideal theory in commutative rings (13A15) Formal power series rings (13F25)

Related Items (32)

Nicely-contractible ideals, z0−ideals and z−ideals in formal series rings in finitely many variables ⋮ Some results on \(S\)-primary ideals of a commutative ring ⋮ Laskerian pairs ⋮ On strongly J-Noetherian rings ⋮ Noetherian-like properties in polynomial and power series rings ⋮ On the planarity of a graph associated to a commutative ring and on the planarity of its complement ⋮ On a spanning subgraph of the annihilating-ideal graph of a commutative ring ⋮ Endoregular modules ⋮ Helson operators and coinvariant subspaces ⋮ On modules satisfying \(S\)-Noetherian spectrum condition ⋮ On the complement of the total zero-divisor graph of a commutative ring ⋮ Noetherian properties in monoid rings. ⋮ On certain distinguished spectral sets ⋮ Second spectrum of modules and spectral spaces ⋮ When are D+M rings Laskerian? ⋮ Unnamed Item ⋮ Some results on a spanning subgraph of the complement of the annihilating-ideal graph of a commutative reduced ring ⋮ Ideals contracted from a Noetherian extension ring ⋮ The Laskerian property in commutative rings ⋮ U-factorization of ideals ⋮ Unnamed Item ⋮ S-Noetherian spectrum condition ⋮ Unnamed Item ⋮ Laskerian Lattices ⋮ Modules and Rings Satisfying (ACCR) ⋮ Endo-Noetherian rings ⋮ The exact zero-divisor graph of a reduced ring ⋮ On \(n\)-absorbing ideals of locally divided commutative rings ⋮ Commutative rings with ACC on n-generated ideals ⋮ Associates, irreducibility, and factorization length in monoid rings with zero divisors ⋮ N-rings and ACC on colon ideals ⋮ Ore extensions over right strongly Hopfian rings.

Cites Work

• Unnamed Item
• Some countability conditions in a commutative ring
• Rings with Noetherian spectrum
• Zero Divisors in Noetherian-Like Rings
• On the Noetherian-like rings of E. G. Evans

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