Strongly Clean Matrices Over Power Series

IF 0.6 Q3 MATHEMATICS

Kyungpook Mathematical Journal Pub Date : 2016-06-23 DOI:10.5666/KMJ.2016.56.2.387

Huanyin Chen, H. Kose, Y. Kurtulmaz

引用次数: 0

Abstract

An n×n matrix A over a commutative ring is strongly clean provided that it can be written as the sum of an idempotent matrix and an invertible matrix that commute. Let R be an arbitrary commutative ring, and let A(x) ∈ Mn ( R[[x]] ) . We prove, in this note, that A(x) ∈ Mn ( R[[x]] ) is strongly clean if and only if A(0) ∈ Mn(R) is strongly clean. Strongly clean matrices over quotient rings of power series are also determined.

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幂级数上的强干净矩阵

交换环上的n×n矩阵A是强清洁的，只要它可以写成幂等矩阵和可逆交换矩阵的和。设R为任意交换环，设A(x)∈Mn (R[[x]])。本文证明，当且仅当A(0)∈Mn(R)是强干净的，则A(x)∈Mn(R [[x]])是强干净的。幂级数商环上的强干净矩阵也被确定。

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

Kyungpook Mathematical Journal MATHEMATICS-

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Kyungpook Mathematical Journal is an international journal devoted to significant research concerning all aspects of mathematics. The journal has a preference for papers having a broad interest. One volume of the journal is published every year. Each volume until volume 42 consisted of two issues; however, starting from volume 43(2003), each volume consists of four issues. Authors should strive for expository clarity and good literary style. Manuscripts should be prepared as follows. The first page must consist of a short descriptive title, followed by the name(s) and address(es) of the author(s) along with an electronic address if available.