Mathematics – Rings and Algebras
Scientific paper
2011-12-07
Mathematics
Rings and Algebras
Scientific paper
The concept of an $I$-matrix in the full $2\times 2$ matrix ring $M_2(R/I)$, where $R$ is an arbitrary UFD and $I$ is a nonzero ideal in $R$, was introduced in \cite{mar}. Moreover a concrete description of the centralizer of an $I$-matrix $\hat B$ in $M_2(R/I)$ as the sum of two subrings $\mathcal S_1$ and $\mathcal S_2$ of $M_2(R/I)$ was also given, where $\mathcal S_1$ is the image (under the natural epimorphism from $M_2(R)$ to $M_2(R/I)$) of the centralizer in $M_2(R)$ of a pre-image of $\hat B$, and where the entries in $\mathcal S_2$ are intersections of certain annihilators of elements arising from the entries of $\hat B$. In the present paper, we obtain results for the case when $I$ is a principal ideal $
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