纯粹数学与应用数学
純粹數學與應用數學
순수수학여응용수학
PURE AND APPLIED MATHEMATICS
2014年
2期
216-220
,共5页
素谱%极大谱%连通性%本原幂等元
素譜%極大譜%連通性%本原冪等元
소보%겁대보%련통성%본원멱등원
prime spectrum%maximal spectrum%connectedness%primitive idempotent
试图刻划交换环的素谱和极大谱的连通分支，为此本文讨论了交换环的本原幂等元与素谱以及极大谱的连通分支的关系。证明了若e 为本原幂等元，则D(e)为SpecA的连通分支。类似地，若 e 为 A 的本原幂等元且 Nil(A)=Rad(A)，则 D(e)为 max A的连通分支。
試圖刻劃交換環的素譜和極大譜的連通分支，為此本文討論瞭交換環的本原冪等元與素譜以及極大譜的連通分支的關繫。證明瞭若e 為本原冪等元，則D(e)為SpecA的連通分支。類似地，若 e 為 A 的本原冪等元且 Nil(A)=Rad(A)，則 D(e)為 max A的連通分支。
시도각화교환배적소보화겁대보적련통분지，위차본문토론료교환배적본원멱등원여소보이급겁대보적련통분지적관계。증명료약e 위본원멱등원，칙D(e)위SpecA적련통분지。유사지，약 e 위 A 적본원멱등원차 Nil(A)=Rad(A)，칙 D(e)위 max A적련통분지。
The main purpose of this paper is trying to character connected components of the prime spectrum and the maximal spectrum of a commutative ring. To this aim, the relationship between primitive idempotents and connected components of the prime spectrum and the maximal spectrum is discussed. It is proved that D(e) is a connected component of SpecA if e is a primitive idempotent of A. Analogously, D(e) is a connected component of max A if e is a primitive idempotent of A and Nil(A)=Rad(A).
