Multilinear identities of the matrix ring
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- by Uri Leron PDF
- Trans. Amer. Math. Soc. 183 (1973), 175-202 Request permission
Abstract:
Let V be a vector space over a field F of zero characteristic, which is acted upon by the symmetric group. Systems of generators for V are constructed, which have special symmetry and skew symmetry properties. This is applied to prove that every multilinear polynomial identity of degree $2n + 1$ which holds in the matrix ring ${F_n}(n > 2)$ is a consequence of the standard identity ${s_{2n}}$. The notions of rigid and semirigid sequences of matrices are defined and treated.References
- A. S. Amitsur and J. Levitzki, Minimal identities for algebras, Proc. Amer. Math. Soc. 1 (1950), 449–463. MR 36751, DOI 10.1090/S0002-9939-1950-0036751-9
- I. N. Herstein, Noncommutative rings, The Carus Mathematical Monographs, No. 15, Mathematical Association of America; distributed by John Wiley & Sons, Inc., New York, 1968. MR 0227205
- Nathan Jacobson, Structure of rings, Revised edition, American Mathematical Society Colloquium Publications, Vol. 37, American Mathematical Society, Providence, R.I., 1964. MR 0222106
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 183 (1973), 175-202
- MSC: Primary 16A42
- DOI: https://doi.org/10.1090/S0002-9947-1973-0332873-3
- MathSciNet review: 0332873