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On New Identities for 3 by 3 Matrices
이우 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.5
In this paper we show that the polynomial of degree 9 called generalized algebraicity is a polynomial identity for 3 × 3 matrices. ([5])
On Formanek's central polynomials
이우 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.3-4
Formanek([2]) proved that Mn(K), the matrix algebra has a nontrivial central polynomial when charK = 0. Also Razmyslov([3]) showed the same result using the essential weak identity. In this article we explicitly compute Formanek’s central polynomial for M₂(C) and M₃(C) and classify the coefficients of the central polynomial.
이우 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5
Nagata[3] and Higman[1] showed that nil-algebra of the nilindex n is nilpotent of finite index. In this paper we show that the bounded degree of the nilpotency is less than or equal to 2n −1. Our proof needs only some elementary fact about Vandermonde determinant, which is much simpler than Nagata’ or Higman’ proof. Nagata[3] and Higman[1] showed that nil-algebra of the nilindex n is nilpotent of finite index. In this paper we show that the bounded degree of the nilpotency is less than or equal to 2n −1. Our proof needs only some elementary fact about Vandermonde determinant, which is much simpler than Nagata’ or Higman’ proof.