Noetherian Rings

Books

An Introduction to Noncommutative Noetherian Rings, Second Edition (with R.B. Warfield, Jr.)

London Math. Soc. Student Text Series, No. 61

Cambridge (2004) Cambridge Univ. Press

Math. Reviews 05b:16001

An Introduction to Noncommutative Noetherian Rings (with R.B. Warfield, Jr.)

London Math. Soc. Student Text Series, No. 16

Cambridge (1989) Cambridge Univ. Press

Zentralblatt 679 (1990) 16001; Math. Reviews 91c:16001;

Bull. London Math. Soc. 100 (1991) 91-93

Expository and Overview Articles

Noetherian Hopf algebras

Glasgow Math. J. 55A (2013) 75-87.

Math. Reviews 3110805; Zentralblatt 1292.16023

Quantized coordinate rings and related noetherian algebras

in Proc. 35th. Symposium on Ring Theory and Representation Theory (Okayama 2002) (Y. Hirano, Ed.), Okayama (2003) Univ. of Okayama, pp. 19-45

Uniform ranks of prime factors of skew polynomial rings

in Ring Theory, Proc. Biennial Ohio State - Denison Conf., 1992 (S.K. Jain and S.T. Rizvi, Eds.), pp. 182-199

Singapore (1993) World Scientific

Math. Reviews 96h:16031; Zentralblatt 853.16034

Simple noetherian rings -- the Zalesskii-Neroslavskii examples

in Ring Theory Waterloo 1978 (D. Handelman and J. Lawrence, Eds.), pp. 118-130

Lecture Notes in Math. No. 734

Berlin (1979) Springer-Verlag

Zentralblatt 412 (1980) 16007; Math. Reviews 81b:16009

The state space of K₀ of a ring

in Ring Theory Waterloo 1978 (D. Handelman and J. Lawrence, Eds.), pp. 91-117

Lecture Notes in Math. No. 734

Berlin (1979) Springer-Verlag

Zentralblatt 417 (1980) 16011; Math. Reviews 81c:16037

Research Articles

Non-affine Hopf algebra domains of Gelfand-Kirillov dimension two (with J.J. Zhang)

Glasgow Math. J. 59 (2017) 563-593

Math Reviews MR3682000; Zentralblatt 1396.16024

Noetherian Hopf algebras

Glasgow Math. J. 55A (2013) 75-87

Math. Reviews MR3110805; Zentralblatt 1292.16023

Noetherian Hopf algebra domains of Gelfand-Kirillov dimension two (with J.J. Zhang)

J. Algebra 324 (2010) 3131-3168

Math. Reviews 12d:16098; Zentralblatt 1228.16030

Homological properties of quantized coordinate rings of semisimple groups (with J. J. Zhang)

Proc. London Math. Soc. (3) 94 (2007) 647-671

Math. Reviews 08e:20077; Zentralblatt 1120.16039

A Dixmier-Moeglin equivalence for Poisson algebras with torus actions

in Algebra and Its Applications (D. V. Huynh, S. K. Jain, and S. R. Lopez-Permouth, Eds.), Contemp. Math. 419 (2006) 131-154

Math. Reviews 08a:17024; Zentralblatt 1147.17017

The closed-point Zariski topology for irreducible representations (with E. S. Letzter)

J. Algebra Applic. 5 (2006) 719-730

Math. Reviews 08c:16007; Zentralblatt 1111.16002

Simplicity of noncommutative Dedekind domains (with J.T. Stafford)

Proc. Amer. Math. Soc. 133 (2005) 681-686

Math. Reviews 05j:16016; Zentralblatt 1065.16001

The graded version of Goldie's theorem (with J.T. Stafford)

in Algebra and its Applications (Athens, OH 1999) (D.V. Huynh, S.K. Jain, and S.T. López-Permouth, Eds.), Contemp. Math. 259 (2000) 237-240

Math. Reviews 01g:16087; Zentralblatt 985.16031

Homological aspects of noetherian P.I. Hopf algebras, and irreducible modules of maximal dimension (with K.A. Brown)

J. Algebra 198 (1997) 240-265

Math. Reviews 99c:16036; Zentralblatt 892.16022

Algebras of bounded finite dimensional representation type (with A.D. Bell)

Glasgow Math. J. 37 (1995) 289-302

Math. Reviews 97c:16019; Zentralblatt 849.16014

Skew polynomial extensions of commutative noetherian Jacobson rings (with E.S. Letzter)

Proc. Amer. Math. Soc. 123 (1995) 1673-1680

Math. Reviews 95g:16029; Zentralblatt 839.16023

Prime ideals in skew and q-skew polynomial rings (with E.S. Letzter)

Memoirs Amer. Math. Soc. No. 521 (1994)

Math. Reviews 94j:16051; Zentralblatt 814 (1995) 16026

An unbounded localizable clique

Contemp. Math. 130 (1992) 145-152

Math. Reviews 93g:16033; Zentralblatt 796.16003

Prime ideals in skew polynomial rings and quantized Weyl algebras

J. Algebra 150 (1992) 324-377

Math. Reviews 93h:16051; Zentralblatt 779.16010

Prime links in differential operator rings

Quart. J. Math. Oxford (2) 42 (1991) 457-487

Zentralblatt 757 (1993) 16010; Math. Reviews 93a:16020

Classical localizability in solvable enveloping algebras and Poincaré-Birkhoff-Witt extensions

J. Algebra 132 (1990) 243-262

Zentralblatt 712 (1991) 16017; Math. Reviews 91j: 16021

Prime ideals in differential operator rings. Catenarity (with K.A. Brown and T.H. Lenagan)

Trans. Amer. Math. Soc. 317 (1990) 749-772

Zentralblatt 692 (1990) 16002; Math. Reviews 90e: 16005

Constructing bad noetherian local domains using derivations (with T.H. Lenagan)

J. Algebra 123 (1989) 478-495

Zentralblatt 692 (1990) 13005; Math. Reviews 90g: 13011

Global dimension of differential operator rings. IV - Simple modules

Forum Math. 1 (1989) 185-200

Zentralblatt 656 (1989) 16001; Math. Reviews 90e: 16041

Linked injectives and Ore localizations

J. London Math. Soc. (2) 37 (1988) 404-420

Zentralblatt 612 (1987) 16005; Math. Reviews 89g: 16002

Localizations of essential extensions (with D.A. Jordan)

Proc. Edinburgh Math. Soc. 31 (1988) 243-247

Zentralblatt 619 (1988) 16001; Math. Reviews 90a: 16004

Uniform rank over differential operator rings and Poincaré-Birkhoff-Witt extensions (with A.D. Bell)

Pacific J. Math. 131 (1988) 13-37

Zentralblatt 598 (1987) 16002; Math. Reviews 88j: 16004

Non-artinian essential extensions of simple modules (with A.H. Schofield)

Proc. Amer. Math. Soc. 97 (1986) 233-236

Zentralblatt 594 (1987) 16009; Math. Reviews 87m: 16029

Patch-continuity of normalized ranks of modules over one-sided noetherian rings

Pacific J. Math. 122 (1986) 83-94

Zentralblatt 549 (1985) 16006; Math. Reviews 87i: 16019

Localizations of injective modules (with D.A. Jordan)

Proc. Edinburgh Math. Soc. 28 (1985) 289-299

Zentralblatt 562 (1985) 16013; Math. Reviews 87c: 16003

Krull versus global dimension in noetherian P.I. rings (with L.W. Small)

Proc. Amer. Math. Soc. 92 (1984) 175-178

Zentralblatt 519 (1984) 16011; Math. Reviews 86d: 16020

Height plus differential dimension in commutative noetherian rings (with T.H. Lenagan and P.C. Roberts)

J. London Math. Soc. (2) 30 (1984) 15-20

Zentralblatt 511 (1984) 13017; Math. Reviews 86e: 13004

Krull and global dimensions of Weyl algebras over division rings (with T.J. Hodges and T.H. Lenagan)

J. Algebra 91 (1984) 334-359

Zentralblatt 558 (1985) 16002; Math. Reviews 86d: 16034

Simple noetherian rings not isomorphic to matrix rings over domains

Communic. in Algebra 12 (1984) 1421-1434

Zentralblatt 537 (1985) 16006; Math. Reviews 85j: 16027

Krull dimension of skew-Laurent extensions (with T.H. Lenagan)

Pacific J. Math. 114 (1984) 109-147

Zentralblatt 496 (1983) 16001; Math. Reviews 86a: 16001

Krull dimension of differential operator rings. IV - Multiple derivations (with T.H. Lenagan)

Proc. London Math. Soc. (3) 47 (1983) 306-336

Zentralblatt 498 (1983) 16001; Math. Reviews 85f: 16026

Centralizers in differential, pseudo-differential, and fractional differential operator rings

Rocky Mtn. J. Math. 13 (1983) 573-618

Zentralblatt 532 (1984) 16002; Math. Reviews 85b: 13039

Krull dimension of differential operator rings. III - Noncommutative coefficients (with T.H. Lenagan)

Trans. Amer. Math. Soc. 275 (1983) 833-859

Zentralblatt 529 (1984) 16001; Math. Reviews 85f: 16025

Primitivity in differential operator rings (with R.B. Warfield, Jr.)

Math. Zeitschrift 180 (1982) 503-523

Zentralblatt 495 (1983) 16002; Math. Reviews 83k: 13018

Krull dimension of differential operator rings (with R.B. Warfield, Jr.)

Proc. London Math. Soc. (3) 45 (1982) 49-70

Zentralblatt 493 (1983) 16004; Math. Reviews 83j: 16032

State spaces of K₀ of noetherian rings (with R.B. Warfield, Jr.)

J. Algebra 71 (1981) 322-378

Zentralblatt 472 (1982) 16005; Math. Reviews 83h: 16019

Incompressible critical modules

Communic. in Algebra 8 (1980) 1845-1851

Zentralblatt 449 (1981) 16021; Math. Reviews 81k: 16027

Simple modules over hereditary noetherian prime rings (with R.B. Warfield, Jr.)

J. Algebra 57 (1979) 82-100

Zentralblatt 422 (1980) 16002; Math. Reviews 80g: 16005

Global dimension of differential operator rings. III

J. London Math. Soc. 17 (1978) 397-409

Zentralblatt 389 (1979) 16015; Math. Reviews 58 (1979) 28072

Global dimension of differential operator rings. II

Trans. Amer. Math. Soc. 209 (1975) 65-85

Zentralblatt 306 (1976) 16018; Math. Reviews 52 (1976) 3244

Global dimension of differential operator rings

Proc. Amer. Math. Soc. 45 (1974) 315-322

Zentralblatt 263 (1974) 13003; Math. Reviews 52 (1976) 3243

Localization and splitting in hereditary noetherian prime rings

Pacific J. Math. 53 (1974) 137-151

Zentralblatt 259 (1974) 16002; Math. Reviews 50 (1975) 7225