Weakly Right IQNN Rings

Yang Lee; Sang Bok Nam; Zhelin Piao∗

doi:10.5666/KMJ.2023.63.2.175

Article

Kyungpook Mathematical Journal 2023; 63(2): 175-186

Published online June 30, 2023

Weakly Right IQNN Rings

Yang Lee, Sang Bok Nam, Zhelin Piao∗

Department of Mathematics, Yanbian University, Yanji 133002, P. R. China and Institute for Applied Mathematics and Optics, Hanbat National University, Daejeon 34158, Korea
e-mail : ylee@pusan.ac.kr

Department of Computer Engineering, Kyungdong University, Geseong 24764, Korea
e-mail : k1sbnam@kduniv.ac.kr

Department of Mathematics, Yanbian University, Yanji 133002, P. R. China
e-mail : zlpiao@ybu.edu.cn

Received: June 11, 2022; Accepted: February 7, 2023

Abstract

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Abstract

In this article we look at the property of a 2 by 2 full matrix ring over the ring of integers, of being weakly right IQNN. This generalisation of the property of being right IQNN arises from products of idempotents and nilpotents. We shown that it is, indeed, a proper generalization of right IQNN. We consider the property of beign weakly right IQNN in relation to several kinds of factorizations of a free algebra in two indeterminates over the ring of integers modulo 2.

Keywords: weakly right IQNN ring, idempotent, nilpotent, 2 by 2 full matrix ring, 2 by 2 upper triangular matrix ring, right IQNN ring