Involutives in Triangular Matrix Rings

Year 2020, Volume: 7 Issue: 1, 91 - 103, 28.06.2020

Tuğba Petik , Leman Hocaoğlu , Halim Özdemir

https://doi.org/10.35193/bseufbd.687316

Abstract

Let R be a commutative ring with identity 1 whose involutives are only -1 and 1, and let M be an upper triangular matrices ring which entries are taken from the ring R. In the study, it is established the necessary and sufficient conditions for an element taken from the ring M  to be involutive. Also, when R is finite, it is given a result determining the number of involutive elements in the ring M, and this result is supported by numerical examples. 

Keywords

Involutive matrices, Triangular matrices, Matrix rings

Üçgensel Matris Halkalarında İnvolutifler

Abstract

R, birimli, involutifleri sadece -1 ve 1 olan bir değişmeli halka ve M, elemanları R halkası üzerinden alınan bir üst üçgensel matrisler halkası olsun. Çalışmada, M halkasından alınan bir elemanın involutif olması için gerek ve yeter koşullar ortaya koyulmaktadır. Ayrıca, R sonlu olduğunda, M halkasındaki involutif elemanların sayısını belirleyen bir sonuç verilmekte ve bu sonuç sayısal örneklerle desteklenmektedir.

Keywords

İnvolutif matrisler, Üçgensel matrisler, Matris halkaları

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