Involutives in Triangular Matrix Rings

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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