MAXIMALITY PRESERVING CONSTRUCTIONS OF MAXIMAL COMMUTATIVE SUBALGEBRAS OF MATRIX ALGEBRA
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Let (R, $m_R$, k) be a local maximal commutative subalgebra of Mn(k) with nilpotent maximal ideal $m_R$. In this paper, we will construct a maximal commutative subalgebra $R^{ST}$ which is isomorphic to R and study some interesting properties related to $R^{ST}$. Moreover, we will introduce a method to construct an algebra in $MC_n$(k) with i($m_R$) = n and dim(R) = n.
Abstract
Let (R, $m_R$, k) be a local maximal commutative subalgebra of Mn(k) with nilpotent maximal ideal $m_R$. In this paper, we will construct a maximal commutative subalgebra $R^{ST}$ which is isomorphic to R and study some interesting properties related to $R^{ST}$. Moreover, we will introduce a method to construct an algebra in $MC_n$(k) with i($m_R$) = n and dim(R) = n.
참고문헌 (10)
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