The symplectic group over a ring with one in its stable range.
B. Kirkwood and B. R. McDonald
Source: Pacific J. Math. Volume 92, Number 1
(1981), 111-125.
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Permanent link to this document: http://projecteuclid.org/euclid.pjm/1102737501
Zentralblatt MATH identifier: 0466.20023
Mathematical Reviews number (MathSciNet): MR618050
References
[1] H. Bass, Algebraic K-theory, Benjamin New York, 1968.
Mathematical Reviews (MathSciNet): MR40:2736
[2] H. Bass, K-theory and stable algebra, Publ. I.H.E.S., 22 (1964), 5-60.
Mathematical Reviews (MathSciNet): MR30:4805
Zentralblatt MATH: 0248.18025
[3] I. G. Connell, Some ring theoretic Schroder-BernsteinTheorem, Trans. Amer. Math. Soc, 132 (1968), 335-351.
Mathematical Reviews (MathSciNet): MR36:5165
Zentralblatt MATH: 0162.04503
[4] D. Estes and J. Ohm, Stable range in commutativerings, J. Algebra, 7 (1967), 343-362.
Mathematical Reviews (MathSciNet): MR36:147
Zentralblatt MATH: 0156.27303
[5] K. R. Goodearl, Von Neumann Regular Rings, Pitman London, 1979
Mathematical Reviews (MathSciNet): MR80e:16011
Zentralblatt MATH: 0411.16007
[6] W. Jehne, Die Struktur der symplektischen Gruppen ilber lokalen und dedekindschen Ringen, Sitzungber, Heidelberg Akad. Wiss. Math. Naturwiss, a (1962/64), 189-235.
Mathematical Reviews (MathSciNet): MR31:275
[7] W. van der Kallen, The K2 of rings with many units, Ann. Scient. Ec. Norm. Sup., 10 (1977), 473-515.
Mathematical Reviews (MathSciNet): MR58:22018
Zentralblatt MATH: 0393.18012
[8] F. Kirchheimer, Die Normalteilerder symplektischenGruppen uber beliebigen lokalen Ringen, J. Algebra, 50 (1978), 228-241.
Mathematical Reviews (MathSciNet): MR58:28209
Zentralblatt MATH: 0368.20030
[9] B. Kirkwood and B. McDonald, The Witt ring of a full ring, J. Algebra, 64 (1980), 148-166.
Mathematical Reviews (MathSciNet): MR82a:10024
Zentralblatt MATH: 0438.13001
[10] B. Kirkwood and B. McDonald, The orthogonal group over a full ring, to appear J. Algebra.
Mathematical Reviews (MathSciNet): MR82h:10035
Zentralblatt MATH: 0448.20047
[11] W. Klingenberg, Symplectic groups over local rings, Amer. J. Math., 85 (1963), 232-240.
Mathematical Reviews (MathSciNet): MR27:3710
Zentralblatt MATH: 0117.27201
[12] V. I. Kopeyko, The stablizationof symplecticgroups over a polynomialring, Math. USSR Sbornik, 34 (1978), 655-669.
[13] B. R. McDonald, Geometric Algebra Over Local Rings, Marcel Dekker, Inc., New York, 1976.
Mathematical Reviews (MathSciNet): MR57:16198
Zentralblatt MATH: 0346.20027
[14] B. McDonald and B. Hershberger, The orthogonal group over a fullring, J. Algebra, 51 (1978), 536-549.
Mathematical Reviews (MathSciNet): MR58:654
Zentralblatt MATH: 0377.15009
[15] B. McDonald, GL2 of rings with many units, Comm. in Algebra, 8(9) (1980), 869-888.
Mathematical Reviews (MathSciNet): MR81k:20068
Zentralblatt MATH: 0436.20031
[16] B. McDonald, The special orthogonal group over a full ring, J. Algebra.
[17] L. McQueen and B. R. McDonald, Automorphismsof the symplecticgroup over a local ring, J. Algebra, 30 (1974), 485-495.
Mathematical Reviews (MathSciNet): MR50:13301
Zentralblatt MATH: 0286.20061
[18] E. F. Robertson, Some properties of a subgroup of SV(R), J. London Math. Soc, (2) 4 (1971), 65-78.
Mathematical Reviews (MathSciNet): MR45:2034
Zentralblatt MATH: 0218.20042
[19] Yu. V. Sosnovskii, Commutatorstructureof symplecticgroup, translated from Matematicheskie Zametki, 24 (1978), 641-648.
[20] J. T. Stafford, Stable structure of noncommutativeNoetherianrings, J. Algebra, 47 (1977), 244-267.
Mathematical Reviews (MathSciNet): MR56:5648
Zentralblatt MATH: 0391.16009
[21] R. Warield, Notes on cancellation, stable range and related topics, 1975.
[22] R. Warield, Stable equivalence of matrices and resolutions, Comm. in Algebra, 6 (17), (1978), 1811-1828.
Mathematical Reviews (MathSciNet): MR80c:16021
Zentralblatt MATH: 0389.16008
[23] R. Warield, Stable generation of modules, Module Theory, Springer-Verlag Lecture
Zentralblatt MATH: 0397.16032
[24] R. B. Warfield, Cancellation of modules and groups and stable range of endomor- phism rings, to appear.
Zentralblatt MATH: 0484.16017
Pacific Journal of Mathematics
