環(huán)上矩陣的性質(zhì)

環(huán)上矩陣的性質(zhì)

摘要

設 是具有單位元的結(jié)合環(huán)， 為 上的矩陣環(huán)．本論文首先根據(jù)矩陣環(huán)的理想和剩余類環(huán)的定義，規(guī)定1個加法和乘法，構(gòu)造出矩陣環(huán)的剩余類環(huán)．其次研究了環(huán)上初等矩陣的1些性質(zhì)，并論證了初等矩陣群為1般線性群的正規(guī)子群，在此基礎上研究環(huán)的 群， 環(huán)及其 群的性質(zhì).
關鍵詞：矩陣環(huán)；剩余類環(huán)；1般線性群；特殊線性群；初等矩陣群

The Properties of Matrix Over Ring

ABSTRACT

Let be a associative ring with identity and be the matrix over . In this paper, Firstly, according to ideal of matrix ring and defines of residue class ring, ruled an addition and an multiplication, constructed a residue class ring of matrix ring. Secondly, We mainly invertigated the properties of elementary matrix group and proven the elementary group is normal subgroup in the general linear group and according to such properties, We discussed the properties of  — group over and —ring over .
Keyword:matrix ring ; residue class ring ; general linear group ; special linear group ; elementary group

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