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Infinite general linear groups over rings. (English) Zbl 0504.20030


MSC:

20G35 Linear algebraic groups over adèles and other rings and schemes
20E15 Chains and lattices of subgroups, subnormal subgroups
16S50 Endomorphism rings; matrix rings
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References:

[1] F. W.Anderson and K. R.Fuller, Rings and Categories of Modules. New York 1974. · Zbl 0301.16001
[2] H. Bass,K-theory and stable algebra. Inst. Hautes Études Sci. Publ. Math.22, 489–544 (1964). · Zbl 0248.18025
[3] J. Dieudonné, Les determinants sur un corps non commutatif. Bull. Soc. Math. France71, 27–45 (1943). · Zbl 0028.33904
[4] I. Golubchik, On the general linear group over an associative ring. Uspekhi Mat. Nauk.28, 179–180 (1973), (Russian).
[5] N.Jacobson, Lectures in Abstract Algebra, Vol. II. New York 1953. · Zbl 0053.21204
[6] F.Kasch, Moduln und Ringe. Stuttgart 1977.
[7] W. Klingenberg, Lineare Gruppen über lokalen Ringen. Amer. J. Math.89, 137–153 (1961). · Zbl 0098.02303 · doi:10.2307/2372725
[8] G. Maxwell, Infinite general linear groups over rings. Trans. Amer. Math. Soc.151, 371–375 (1970). · Zbl 0213.31003 · doi:10.1090/S0002-9947-1970-0263932-9
[9] B. R. McDonald,GL 2 of rings with many units. Comm. Algebra8, 869–888 (1980). · Zbl 0436.20031 · doi:10.1080/00927878008822495
[10] A. Rosenberg, The structure of the infinite general linear group. Ann. Math.68, 278–294 (1958). · Zbl 0128.25501 · doi:10.2307/1970248
[11] W. Sierpinski, Cardinal and Ordinal Numbers. Polska Akademia Nauk., Warszawa 1958.
[12] J. S. Wilson, The normal and subnormal structure of general linear groups. Proc. Cambridge Philos. Soc.71, 163–177 (1972). · Zbl 0237.20044 · doi:10.1017/S0305004100050416
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