Rings without identity which are Morita equivalent to regular rings

Pere Ara

Rings without identity which are Morita equivalent to regular rings

Pere Ara

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

11 Citations (Scopus)

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. © AMSS CAS 2004.

Original language	English
Pages (from-to)	533-540
Journal	Algebra Colloquium
Volume	11
Issue number	4
Publication status	Published - 1 Dec 2004

Keywords

Morita equivalence
Non-unital rings
Von Neumann regular rings

Cite this

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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.",

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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

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

Abstract

Keywords

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