The minimal prime spectrum of rings with annihilator conditions.

DOI10.1016/J.JPAA.2009.01.005zbMath1218.16001OpenAlexW1964421873MaRDI QIDQ1013119

Pace P. Nielsen, Yang Lee, Nam Kyun Kim, Chan Yong Hong

Publication date: 16 April 2009

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2009.01.005

zbMATH Keywords

semiprime ringsright annihilatorsfinitely generated idealsminimal prime idealsreduced ringsminimal prime spectraright annihilator condition

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Ordinary and skew polynomial rings and semigroup rings (16S36) Prime and semiprime associative rings (16N60) Ideals in associative algebras (16D25) Topological and ordered rings and modules (16W80) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (7)

Annihilator condition does not pass to polynomials and power series ⋮ A sheaf representation of principally quasi-Baer \(\ast\)-rings ⋮ Minimal prime ideals of reduced rings ⋮ Unnamed Item ⋮ Zariski compactness of minimal spectrum and flat compactness of maximal spectrum ⋮ On the lattice of annihilator ideals and its applications ⋮ On annihilator ideals in skew power series rings

Cites Work

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• Space of minimal prime ideals of a ring without nilpotent elements
• Exercises in modules and rings.
• The minimal prime spectrum of a reduced ring
• Commutative coherent rings
• Annihilation of ideals in commutative rings
• Armendariz rings and reduced rings
• Rings with property (A) and their extensions.
• Some conditions on commutative semiprime rings
• On a representation of a strongly harmonic ring by sheaves
• Armendariz and Reduced Rings
• Spectral spacess and non-commutative rings
• Two annihilator conditions:property(A)and(A.C.)
• Weakly regular rings
• Prime Ideals and Sheaf Representation of a Pseudo Symmetric Ring
• SKEW POLYNOMIAL RINGS OVER SEMIPRIME RINGS
• On ideals consisting entirely of zero divisors
• NOETHERIAN SEMIGROUP ALGEBRAS
• The Space of Minimal Prime Ideals of a Commutative Ring
• Sur la compacité du spectre minimal d'un anneau

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