Müller's question on semi-perfect complete hereditary Noetherian prime rings

Pham Ngoc Ánh; Dolors Herbera

doi:10.1017/S0013091504001099

Müller's question on semi-perfect complete hereditary Noetherian prime rings

Pham Ngoc Ánh, Dolors Herbera

Departament de Matemàtiques

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Resum

A positive answer to a question of Müller is given: any semi-perfect complete hereditary Noetherian prime ring R has a weakly symmetric self-duality sending every ideal I to its cycle-neighbour X. Consequently, the factor rings R/I and R/X are isomorphic without using the 1984 results of Dischinger and Müller.

Idioma original	Anglès
Pàgines (de-a)	567-573
Revista	Proceedings of the Edinburgh Mathematical Society
Volum	49
Número	3
DOIs	https://doi.org/10.1017/S0013091504001099
Estat de la publicació	Publicada - 1 d’oct. 2006

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10.1017/S0013091504001099

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title = "M{\"u}ller's question on semi-perfect complete hereditary Noetherian prime rings",

abstract = "A positive answer to a question of M{\"u}ller is given: any semi-perfect complete hereditary Noetherian prime ring R has a weakly symmetric self-duality sending every ideal I to its cycle-neighbour X. Consequently, the factor rings R/I and R/X are isomorphic without using the 1984 results of Dischinger and M{\"u}ller.",

keywords = "Hereditary, Injective modules, Localizations, Morita duality, Noetherian prime rings, Quotient rings",

author = "{\'A}nh, {Pham Ngoc} and Dolors Herbera",

year = "2006",

month = oct,

day = "1",

doi = "10.1017/S0013091504001099",

language = "English",

volume = "49",

pages = "567--573",

journal = "Proceedings of the Edinburgh Mathematical Society",

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T1 - Müller's question on semi-perfect complete hereditary Noetherian prime rings

AU - Ánh, Pham Ngoc

AU - Herbera, Dolors

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N2 - A positive answer to a question of Müller is given: any semi-perfect complete hereditary Noetherian prime ring R has a weakly symmetric self-duality sending every ideal I to its cycle-neighbour X. Consequently, the factor rings R/I and R/X are isomorphic without using the 1984 results of Dischinger and Müller.

AB - A positive answer to a question of Müller is given: any semi-perfect complete hereditary Noetherian prime ring R has a weakly symmetric self-duality sending every ideal I to its cycle-neighbour X. Consequently, the factor rings R/I and R/X are isomorphic without using the 1984 results of Dischinger and Müller.

KW - Hereditary

KW - Injective modules

KW - Localizations

KW - Morita duality

KW - Noetherian prime rings

KW - Quotient rings

U2 - 10.1017/S0013091504001099

DO - 10.1017/S0013091504001099

M3 - Article

SN - 0013-0915

VL - 49

SP - 567

EP - 573

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

IS - 3

ER -

Müller's question on semi-perfect complete hereditary Noetherian prime rings

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