On cleanness of von Neumann algebras

被引：0

作者：

Cui, Lu ^{[1
,4
]}

Huang, Linzhe ^{[2
]}

Wu, Wenming ^{[3
]}

Yuan, Wei ^{[1
,4
]}

Zhang, Hanbin ^{[5
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China

[2] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

[3] Chongqing Normal Univ, Sch Math Sci, Chongqing 401331, Peoples R China

[4] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

[5] Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai 519082, Guangdong, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2022年 / 509卷 / 02期

关键词：

Von Neumann algebras; Clean rings; Idempotents; Projections; C-ASTERISK-ALGEBRAS; EXCHANGE RINGS; PROJECTIVE-MODULES; FREDHOLM THEORIES; CANCELLATION;

D O I：

10.1016/j.jmaa.2021.125969

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A unital ring is called clean (resp. strongly clean) if every element can be written as the sum of an invertible element and an idempotent (resp. an invertible element and an idempotent that commutes). T.Y. Lam proposed a question: which von Neumann algebras are clean as rings? In this paper, we characterize strongly clean von Neumann algebras and prove that all finite von Neumann algebras and all separable infinite factors are clean. (C)& nbsp;2021 Elsevier Inc. All rights reserved.

引用

页数：21

共 40 条

[1] Characterizations of Gelfand Rings Specially Clean Rings and their Dual Rings [J].

Aghajani, Mohsen ;

Tarizadeh, Abolfazl .

RESULTS IN MATHEMATICS, 2020, 75 (03)

[2] Classes of Almost Clean Rings [J].

Akalan, Evrim ;

Vas, Lia .

ALGEBRAS AND REPRESENTATION THEORY, 2013, 16 (03) :843-857

[3]

[Anonymous], 1991, von Neumann regular rings

[4] Separative cancellation for projective modules over exchange rings [J].

Ara, P ;

Goodearl, KR ;

O'Meara, KC ;

Pardo, E .

ISRAEL JOURNAL OF MATHEMATICS, 1998, 105 (1) :105-137

[5] K1 of separative exchange rings and C*-algebras with real rank zero [J].

Ara, P ;

Goodearl, KR ;

O'Meara, KC ;

Raphael, R .

PACIFIC JOURNAL OF MATHEMATICS, 2000, 195 (02) :261-275

[6]

Bezhanishvili G, 2013, THEOR APPL CATEG, V28, P435

[7] A gentle guide to the basics of two projections theory [J].

Boettcher, A. ;

Spitkovsky, I. M. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (06) :1412-1459

[8] FREDHOLM THEORIES IN VON NEUMANN ALGEBRAS .I. [J].

BREUER, M .

MATHEMATISCHE ANNALEN, 1968, 178 (03) :243-&

[9] FREDHOLM THEORIES IN VON NEUMANN ALGEBRAS .2. [J].

BREUER, M .

MATHEMATISCHE ANNALEN, 1969, 180 (04) :313-&

[10] C-STAR-ALGEBRAS OF REAL RANK ZERO [J].

BROWN, LG ;

PEDERSEN, GK .

JOURNAL OF FUNCTIONAL ANALYSIS, 1991, 99 (01) :131-149

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