Graded central polynomials for the algebra M n (K)

Abstract

Let M n (K) be the algebra of all n × n matrices over an infinite field K. This algebra has a natural Z n -grading and a natural Z-grading. Finite bases for its Z n -graded identities and for its Z-graded identities are known. In this paper we describe finite generating sets for the Z n -graded and for the Z-graded central polynomials for M n (K)

Primeness property for graded central polynomials of verbally prime algebras

“…Proposition 3. 7. Let A be algebra M n (F ) with an elementary grading induced by the n-tuple (h 1 , .…”

“…Lemma 5. 7. Let A = A 0 ⊕ A 1 denote the algebra M a,b (E) with its canonical Z 2grading and let f (x 1 , .…”

“…, h s ) such that a i ∈ R hi . This scalar will be denoted ǫ R h,m hence we have 7. Let f (x 1,g1 , .…”

“…The graded identities and central polynomials of matrix algebras have been described for various gradings. For example, with the canonical Z and Z n , central polynomials were described in [7] and more generally in [1] with crossed product gradings. It is then a natural question to consider the analogous primeness property for the graded polynomials of M n (F ).…”

Polinomios centrais para algebras graduadas

“…Para cada uma delas foram apresentados geradores do respectivo T -espaço Z 2 -graduado de polinômios centrais. Neste capítulo vamos apresentar as descrições feitas em [7] dos polinômios centrais Zn-graduados e dos . 'l-graduados para a álgebra Mn(K).…”