Polynomial Detection of Matrix Subalgebras

On Matrix Subalgebras Not Satisfying an Identity Of

Abstract. The Amitsur-Levitski theorem asserts that Mn(F ) satisfies a polynomial identity of degree 2n. (Here, F is a field and Mn(F ) is the algebra of n × n matrices over F ). It is easy to give examples of subalgebras of Mn(F ) that do satisfy an identity of lower degree and subalgebras of Mn(F ) that satisfy no polynomial identity of degree ≤ 2n− 2. Our aim in this paper is to give a full ...

ON SUBALGEBRAS OF n× n MATRICES NOT SATISFYING IDENTITIES OF DEGREE 2n− 2

The Amitsur-Levitzki theorem asserts that Mn(F ) satisfies a polynomial identity of degree 2n. (Here, F is a field and Mn(F ) is the algebra of n × n matrices over F ). It is easy to give examples of subalgebras of Mn(F ) that do satisfy an identity of lower degree and subalgebras of Mn(F ) that satisfy no polynomial identity of degree ≤ 2n − 2. In this paper we prove that the subalgebras of n ...

Canonical bases for subalgebras of factor algebras

We introduce canonical bases for subalgebras of quotients of the commutative and non-commutative polynomial ring. The usual theory for Gröbner bases and its counterpart for subalgebras of polynomial rings, also called SAGBI bases, are combined to obtain a tool for computation in subalgebras of factor algebras.

Determination of a Matrix Function in the Form of f(A)=g(q(A)) Where g(x) Is a Transcendental Function and q(x) Is a Polynomial Function of Large Degree Using the Minimal Polynomial

Matrix functions are used in many areas of linear algebra and arise in numerical applications in science and engineering. In this paper, we introduce an effective approach for determining matrix function f(A)=g(q(A)) of a square matrix A, where q is a polynomial function from a degree of m and also function g can be a transcendental function. Computing a matrix function f(A) will be time- consu...

Differential Polynomial Rings of Triangular Matrix Rings