Abstract
Let (R, <TEX>$m_R$</TEX>, k) be a local maximal commutative subalgebra of <TEX>$M_n$</TEX>(k) with nilpotent maximal ideal <TEX>$m_R$</TEX>. In this paper, we will construct a maximal commutative subalgebra <TEX>$R^{ST}$</TEX> which is isomorphic to R and study some interesting properties related to <TEX>$R^{ST}$</TEX>. Moreover, we will introduce a method to construct an algebra in <TEX>$MC_n$</TEX>(k) with i(<TEX>$m_R$</TEX>) = n and dim(R) = n.
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