Certain Clean Decompositions for Matrices over Local Rings

Yosum Kurtulmaz; Handan Köse; Huanyin Chen*

doi:10.5666/KMJ.2023.63.4.561

Article

Kyungpook Mathematical Journal 2023; 63(4): 561-569

Published online December 31, 2023

Certain Clean Decompositions for Matrices over Local Rings

Yosum Kurtulmaz, Handan Köse, Huanyin Chen*

Department of Mathematics, Bilkent University, Ankara, Turkey
e-mail : yosum@fen.bilkent.edu.tr

Department of Mathematics, Ahi Evran University, Kirşehir, Turkey
e-mail : handan.kose@ahievran.edu.tr

School of Big Data, Fuzhou University of International Studies and Trade, Fuzhou 350202, China
e-mail : huanyinchenfz@163.com

Received: December 15, 2022; Revised: July 21, 2023; Accepted: July 25, 2023

Abstract

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Abstract

An element a∈R is strongly rad-clean provided that there exists an idempotent e∈R such that a−e∈U(R), ae=ea and eae∈J(eRe). In this article, we completely determine when a 2×2 matrix over a commutative local ring is strongly rad clean. An application to matrices over power-series is also given.

Keywords: Strongly clean matrix, Strongly rad-clean matrix, Local ring, Power-series