Rings without identity which are Morita equivalent to regular rings

Pere Ara

Rings without identity which are Morita equivalent to regular rings

Pere Ara

Departament de Matemàtiques

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Resum

We prove that von Neumann regularity is not a Morita invariant property for non-unital rings. This contrasts heavily with the unital case. Moreover, we give an internal characterization of the idempotent rings which are Morita equivalent to a von Neumann regular ring. We also show that an s-unital ring Morita equivalent to a von Neumann regular ring is von Neumann regular too. © AMSS CAS 2004.

Idioma original	Anglès
Pàgines (de-a)	533-540
Revista	Algebra Colloquium
Volum	11
Número	4
Estat de la publicació	Publicada - 1 de des. 2004

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https://www.scopus.com/pages/publications/28044458736

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title = "Rings without identity which are Morita equivalent to regular rings",

abstract = "We prove that von Neumann regularity is not a Morita invariant property for non-unital rings. This contrasts heavily with the unital case. Moreover, we give an internal characterization of the idempotent rings which are Morita equivalent to a von Neumann regular ring. We also show that an s-unital ring Morita equivalent to a von Neumann regular ring is von Neumann regular too. {\textcopyright} AMSS CAS 2004.",

keywords = "Morita equivalence, Non-unital rings, Von Neumann regular rings",

author = "Pere Ara",

year = "2004",

month = dec,

day = "1",

language = "English",

volume = "11",

pages = "533--540",

journal = "Algebra Colloquium",

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TY - JOUR

T1 - Rings without identity which are Morita equivalent to regular rings

AU - Ara, Pere

PY - 2004/12/1

Y1 - 2004/12/1

N2 - We prove that von Neumann regularity is not a Morita invariant property for non-unital rings. This contrasts heavily with the unital case. Moreover, we give an internal characterization of the idempotent rings which are Morita equivalent to a von Neumann regular ring. We also show that an s-unital ring Morita equivalent to a von Neumann regular ring is von Neumann regular too. © AMSS CAS 2004.

AB - We prove that von Neumann regularity is not a Morita invariant property for non-unital rings. This contrasts heavily with the unital case. Moreover, we give an internal characterization of the idempotent rings which are Morita equivalent to a von Neumann regular ring. We also show that an s-unital ring Morita equivalent to a von Neumann regular ring is von Neumann regular too. © AMSS CAS 2004.

KW - Morita equivalence

KW - Non-unital rings

KW - Von Neumann regular rings

UR - https://www.scopus.com/pages/publications/28044458736

M3 - Article

SN - 1005-3867

VL - 11

SP - 533

EP - 540

JO - Algebra Colloquium

JF - Algebra Colloquium

IS - 4

ER -

Rings without identity which are Morita equivalent to regular rings

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