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.
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

The Dixmier-Moeglin equivalence and a Gel'fand-Kirillov problem for Poisson polynomial algebras (with S. Launois)
Bull. Soc. Math. France 139 (2011) 1-39
Math. Reviews 12e:17045; Zentralblatt 1226.17016
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
Poisson structures on affine spaces and flag varieties. II. (with M. Yakimov)
Trans. Amer. Math. Soc. 361 (2009) 5753-5780
Math. Reviews 10k:14092; Zentralblatt 1179.53087
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
Poisson structures on affine spaces and flag varieties. I. Matrix affine Poisson space (with K. A. Brown and M. Yakimov)
Advances in Math. 206 (2006) 567-629
Math. Reviews 07k:14094; Zentralblatt 1105.53062
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

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goodearl@math.ucsb.edu

Last Modified: August 2013

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