Von Neumann Regular Rings

Book

Von Neumann Regular Rings

Monographs and Studies in Math., No. 4

London (1979) Pitman

Zentralblatt 411 (1980) 16007; Math. Reviews 80e:16011;

Bull. Amer. Math. Soc. 3 (1980) 752-757

Second Edition:

Malabar, FL (1991) Krieger

Zentralblatt 749 (1992) 16001; Math. Reviews 93m:16006

Expository and Overview Articles

Von Neumann regular rings and direct sum decomposition problems

in Abelian Groups and Modules, Padova 1994 (A. Facchini and C. Menini, Eds.), pp. 249-255

Dordrecht (1995) Kluwer

Zentralblatt 841.16008; Math. Reviews MR1378203

Partially ordered Grothendieck groups

in Algebra and Its Applications (H.L. Manocha and J.B. Srivastava, Eds.), pp. 71-90

New York (1984) Dekker

Zentralblatt 544 (1985) 16011; Math. Reviews MR0750851

Von Neumann regular rings: Connections with functional analysis

Bull. Amer. Math. Soc. 4 (1981) 125-134

Zentralblatt 467 (1982) 16020; Math. Reviews 82d:16012

Regular rings and rank functions

in Noncommutative Ring Theory Kent State 1975 (J.H. Cozzens and F.L. Sandomierski, Eds.), pp. 83-104

Lecture Notes in Math. No. 545

Berlin (1976) Springer-Verlag

Zentralblatt 341 (1977) 16006; Math. Reviews 55 (1978) 401

Research Articles

The separativity problem in terms of varieties and diagonal reduction (with P. Ara, P.P. Nielsen, E. Pardo, and F. Perera)

in NonCommutative Rings and their Applications, VIII (A. Laghribi and A. Leroy, eds.)

Contemp. Math.

Regular ring properties degraded through inverse limits (with P. Ara, K.C. O'Meara, E. Pardo, and F. Perera)

J. Algebra 664 (2025) 365-397

The realization problem for some wild monoids and the Atiyah problem (with P. Ara)

Trans. Amer. Math. Soc. 369 (2017) 5665-5710

Math Reviews MR3646775; Zentralblatt 1405.16013

The complete dimension theory of partially ordered systems with equivalence and orthogonality (with F. Wehrung)

Memoirs Amer. Math. Soc. No. 831 (2005) viii+1-117

Zentralblatt 1075.06001; Math. Reviews 06d:06001

K₀ of purely infinite simple regular rings (with P. Ara and E. Pardo)

K-Theory 26 (2002) 69-100

Zentralblatt 1012.16013; Math. Reviews 04e:19001

Representations of distributive semilattices in ideal lattices of various algebraic structures (with F. Wehrung)

Algebra Universalis 45 (2001) 71-102

Math. Reviews 02g:06008; Zentralblatt 1039.06003

K₁ of separative exchange rings and C*-algebras with real rank zero (with P. Ara, K. C. O'Meara, and R. Raphael)

Pacific J. Math. 195 (2000) 261-275

Math. Reviews 01m:46155; Zentralblatt 1108.46311

Separative cancellation for projective modules over exchange rings (with P. Ara, K. C. O'Meara, and E. Pardo)

Israel J. Math. 105 (1998) 105-137

Math. Reviews 99g:16006; Zentralblatt 908.16002

Diagonalization of matrices over regular rings (with P. Ara, K. C. O'Meara, and E. Pardo)

Linear Algebra Applic. 265 (1997) 147-163

Zentralblatt 883.15006; Math. Reviews 98i:16013

Torsion in K₀ of unit-regular rings

Proc. Edinburgh Math. Soc. 38 (1995) 331-341

Zentralblatt 821 (1995) 16008; Math. Reviews 97c:16010

K-theoretically simple von Neumann regular rings (with P. Ara, E. Pardo, and D.V. Tyukavkin)

J. Algebra 174 (1995) 531-552

Math. Reviews 96g:16012; Zentralblatt 837.16008

K₀ of regular rings with bounded index of nilpotence

in Abelian Group Theory and Related Topics (R. Göbel, P. Hill, and W. Liebert, Eds.)

Contemp. Math. 171 (1994) 173-199

Math. Reviews 95h:16008; Zentralblatt 816 (1995) 16012

Free and residually artinian regular rings (with P. Menal and J. Moncasi)

J. Algebra 156 (1993) 407-432

Math. Reviews 94f:16025; Zentralblatt 780.16006

The almost isomorphism relation for simple regular rings (with P. Ara)

Publ. Mat. (Barcelona) 36 (1992) 369-388

Math. Reviews 94f:16024; Zentralblatt 792.16013

Cancellation of finitely generated modules over regular rings (with J. Moncasi)

Osaka J. Math. 26 (1989) 679-685

Zentralblatt 716 (1991) 16007; Math. Reviews 91b:16013

Classification of ring and C*-algebra direct limits of finite-dimensional semisimple real algebras (with D.E. Handelman)

Memoirs Amer. Math. Soc. No. 372 (1987) vii + 1-147

Zentralblatt 629 (1988) 46053; Math. Reviews 88k: 46067

Tensor products of dimension groups and K₀ of unit-regular rings (with D.E. Handelman)

Canadian J. Math. 38 (1986) 633-658

Zentralblatt 608 (1987) 16027; Math. Reviews 87i:16043

Directly finite aleph-nought-continuous regular rings

Pacific J. Math. 100 (1982) 105-122

Zentralblatt 453 (1981) 16007; Math. Reviews 83j:16022

Metrically complete regular rings

Trans. Amer. Math. Soc. 272 (1982) 275-310

Zentralblatt 494 (1983) 16007; Math. Reviews 83i:16014

Extensions of simple by simple unit-regular rings

in Ring Theory Antwerp 1980 (F. Van Oystaeyen, Ed.), pp. 42-58

Lecture Notes in Math. No. 825

Berlin (1980) Springer-Verlag

Zentralblatt 446 (1981) 16010; Math. Reviews 82m:16009

Affine representations of Grothendieck groups and applications to Rickart C*-algebras and Aleph₀-continuous regular rings (with D.E. Handelman and J.W. Lawrence)

Memoirs Amer. Math. Soc. No. 234 (1980) vii+1-163

Zentralblatt 435 (1981) 16005; Math. Reviews 81f:16040

Artinian and noetherian modules over regular rings

Communic. in Algebra 8 (1980) 477-504

Zentralblatt 438 (1981) 16006; Math. Reviews 81g:16015

Homogenization of regular rings of bounded index (with D.E. Handelman)

Pacific J. Math. 84 (1979) 63-78

Zentralblatt 388 (1979) 16012; Math. Reviews 81f:16020

Centers of regular self-injective rings

Pacific J. Math. 76 (1978) 381-395

Zentralblatt 351 (1978) 16007; Math. Reviews 58 (1979) 28059

Completions of regular rings. II

Pacific J. Math. 72 (1977) 423-459

Zentralblatt 337 (1977) 16002; Math. Reviews 57 (1979) 16354

Algebraic representations of Choquet simplexes

J. Pure Appl. Algebra 11 (1977) 111-130

Zentralblatt 372 (1978) 16009; Math. Reviews 57 (1979) 6147

Dimension theory for nonsingular injective modules (with A.K. Boyle)

Memoirs Amer. Math. Soc. No. 177 (1976) vii+1-112

Zentralblatt 335 (1977) 16024; Math. Reviews 55 (1978) 3001

Completions of regular rings

Math. Annalen 220 (1976) 229-252

Zentralblatt 321 (1976) 16010; Math. Reviews 53 (1977) 13296

Rank functions and K₀ of regular rings (with D. Handelman)

J. Pure Appl. Algebra 7 (1976) 195-216

Zentralblatt 321 (1976) 16009; Math. Reviews 52 (1976) 10794

Simple self-injective rings (with D. Handelman)

Communic. in Algebra 3 (1975) 797-834

Zentralblatt 311 (1976) 16029; Math. Reviews 52 (1976) 498

Simple regular rings and rank functions

Math. Annalen 214 (1975) 267-287

Zentralblatt 285 (1975) 16008; Math. Reviews 53 (1977) 13295

Simple self-injective rings need not be artinian

Communic. in Algebra 2 (1974) 83-89

Zentralblatt 267 (1974) 16011; Math. Reviews 50 (1975) 402

Prime ideals in regular self-injective rings. II

J. Pure Appl. Algebra 3 (1973) 357-373

Zentralblatt 272 (1974) 16016; Math. Reviews 48 (1974) 8561

Prime ideals in regular self-injective rings

Canadian J. Math. 25 (1973) 829-839

Zentralblatt 229 (1972) 16021; Math. Reviews 48 (1974) 4037