On adequacy of full matrices

Q3 Mathematics
A. Gatalevych, V. Shchedryk
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引用次数: 0

Abstract

This paper deals with the following question:whether a ring of matrices or classes of matrices over an adequate ring or elementary divisor ring inherits the property of adequacy? The property to being adequate in matrix rings over adequate and commutative elementary divisor rings is studied.Let us denote by $\mathfrak{A}$ and $\mathfrak{E}$ an adequate and elementary divisor domains, respectively. Also $\mathfrak{A}_2$ and $\mathfrak{E}_2$ denote a rings of $2 \times 2$ matrices over them. We prove that full nonsingular matrices from $\mathfrak{A}_2$ are adequate in $\mathfrak{A}_2$ and full singular matrices from $\mathfrak{E}_2$ are adequate in the set of full matrices in $\mathfrak{E}_2$.
关于满矩阵的充分性
本文讨论了一个矩阵环或矩阵类在充分环或初等除数环上是否继承了充分性?研究了矩阵环在适足交换初等因子环上的适足性。让我们分别用$\mathfrak{A}$和$\mathfrak{E}$表示一个充分的和初等的除数域。同样,$\mathfrak{A}_2$和$\mathfrak{E}_2$表示在它们上面由$2 \乘以2$矩阵组成的环。证明了$\mathfrak{A}_2$中的满非奇异矩阵在$\mathfrak{A}_2$中是充分的,$\mathfrak{E}_2$中的满奇异矩阵在$\mathfrak{E}_2$中的满矩阵集合中是充分的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Matematychni Studii
Matematychni Studii Mathematics-Mathematics (all)
CiteScore
1.00
自引率
0.00%
发文量
38
期刊介绍: Journal is devoted to research in all fields of mathematics.
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