Invertible ideals and existence of quotient rings

DOI10.1080/00927879808826254zbMath0907.16006OpenAlexW2078103382MaRDI QIDQ4392653

R. M. Lissaman, Charudatta R. Hajarnavis

Publication date: 3 March 1999

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

Full work available at URL: https://doi.org/10.1080/00927879808826254

zbMATH Keywords

regular elementsAsano ordersintegral idealsclassical quotient ringsfully bounded Noetherian ringsdirect sums of prime ringsDedekind ordersfinitely-generated torsion modules

Mathematics Subject Classification ID

Ideals in associative algebras (16D25) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc. (16E60) Noetherian rings and modules (associative rings and algebras) (16P40) Localization and associative Noetherian rings (16P50)

Related Items (2)

Internal characterizations of non-prime dedekind orders ⋮ Global theory of lattice-finite Noetherian rings.

Cites Work

• Reduced rank in Noetherian rings
• Non-commutative Dedekind rings
• Modules over Dedekind prime rings
• Idealizers and hereditary Noetherian prime rings
• Global dimension of fully bounded noetherian rings
• Three examples concerning the ore condition in Noetherian rings
• Regularity of Zero Divisors
• Les t-anneaux, la condition (H) de gabriel et ses consequences
• Internal characterizations of non-prime dedekind orders
• Asano Orders
• Bounded Asano Orders are Hereditary
• A Note on Dedekind Prime Rings

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