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Ricardo Andrade
Ricardo Andrade
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I will be so thankful if some onesomeone can help me aboutwith the following question.

Is it possible to obtain all maximal centralizers in the full matrix ring, $M_n(F)$, for an arbitrary finite field $F$? Here, where by maximal centralizer I mean: $C=C_R(x)$ is maximal if $C\subseteq C_R(y)$, then $C=C_R(y)$ or $y\in Z(R)$.

In Akbari et al., Linear Alg. App. 390 (2004) 345-355, in Lemmalemma 3 determines alldetermines all centralizers with maximum dimension. So some of the maximal centralizers are determined. Is it true that the set of centralizercentralizers with maximum dimension and the set of maximal centralizers are equal? Hamid

Hamid.

I will be so thankful if some one help me about the following question.

Is it possible to obtain all maximal centralizers in full matrix ring, $M_n(F)$, for arbitrary finite field $F$, where by maximal centralizer I mean $C=C_R(x)$ is maximal if $C\subseteq C_R(y)$, then $C=C_R(y)$ or $y\in Z(R)$.

In Akbari et al., Linear Alg. App. 390 (2004) 345-355, in Lemma 3 determines all centralizers with maximum dimension. So some of maximal centralizers are determined. Is it true that the set of centralizer with maximum dimension and the set of maximal centralizers are equal? Hamid.

I will be so thankful if someone can help me with the following question.

Is it possible to obtain all maximal centralizers in the full matrix ring, $M_n(F)$, for an arbitrary finite field $F$? Here, by maximal centralizer I mean: $C=C_R(x)$ is maximal if $C\subseteq C_R(y)$, then $C=C_R(y)$ or $y\in Z(R)$.

In Akbari et al., Linear Alg. App. 390 (2004) 345-355, lemma 3 determines all centralizers with maximum dimension. So some of the maximal centralizers are determined. Is it true that the set of centralizers with maximum dimension and the set of maximal centralizers are equal?

Hamid.

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Hamid
Hamid
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Maximal centralizer in full matrix ring

I will be so thankful if some one help me about the following question.

Is it possible to obtain all maximal centralizers in full matrix ring, $M_n(F)$, for arbitrary finite field $F$, where by maximal centralizer I mean $C=C_R(x)$ is maximal if $C\subseteq C_R(y)$, then $C=C_R(y)$ or $y\in Z(R)$.

In Akbari et al., Linear Alg. App. 390 (2004) 345-355, in Lemma 3 determines all centralizers with maximum dimension. So some of maximal centralizers are determined. Is it true that the set of centralizer with maximum dimension and the set of maximal centralizers are equal? Hamid.