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The invariant theory of \(n\times n\) matrices. (English) Zbl 0331.15021

MSC:
15A72 Vector and tensor algebra, theory of invariants
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[1] Artin, M, On Azumaya algebras and finite dimensional representations of rings, J. algebra, 11, 532-563, (1969) · Zbl 0222.16007
[2] Doubilet, P; Rota, G.C; Stein, J, On the foundations of combinational theory. IX. combinational methods in invariant theory, (), 185-216 · Zbl 0426.05009
[3] \scE. Formanek, A new proof of the theorem of Amitsur Levitsky, preprint. · Zbl 0289.16016
[4] \scE. Formanek and C. Procesi, Mumford’s conjecture for GL(n, k), preprint. · Zbl 0346.20021
[5] Grace, J.H; Young, A, The algebra of invariants, (1903), Cambridge Univ. Press New York · JFM 34.0114.01
[6] Jacobson, N, Structure of rings, () · JFM 65.1131.01
[7] Procesi, C, Central polynomials and finite-dimensional representations of rings, () · Zbl 0948.16012
[8] Procesi, C, Finite-dimensional representations of algebras, Israel J. math., 19, 169-182, (1974) · Zbl 0297.16011
[9] Procesi, C, Rings with polynomial identities, (1973), Dekker New York, No. 17 · Zbl 0262.16018
[10] \scC. Procesi and M. Schacher, A non commutative real Nullstellensatz and Hilbert 17th problem, preprint. · Zbl 0347.16010
[11] Rowen, L, Standard polynomials in matrix algebras, Trans. amer. math. soc., 190, 253-284, (1974) · Zbl 0286.16012
[12] Spencer, A.J.M, Theory of invariants, () · Zbl 0339.15012
[13] Spencer, A.J.M; Rivlin, R.S, The theory of matrix polynomials and its applications to the mechanics of isotropic continua, Arch. rat. mech. anal., 2, 309-336, (1958) · Zbl 0095.25101
[14] Spencer, A.J.M; Rivlin, R.S, Finite integrity bases for five or fewer symmetric 3 × 3 matrices, Arch. rat. mech. anal., 2, 435-446, (1959) · Zbl 0095.25102
[15] Spencer, A.J.M; Rivlin, R.S, Further results in the theory of matrix polynomials, Arch. rat. mech. anal., 4, 214-230, (1960) · Zbl 0095.25103
[16] Weyl, H, The classical groups, (1946), Princeton Univ. Press Princeton, N.J · JFM 65.0058.02
[17] Haboush, W.J, Reductive groups are geometrically reductive, Ann. math., 102, 67-83, (1975) · Zbl 0316.14016
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