数学杂志
數學雜誌
수학잡지
JOURNAL OF MATHEMATICS
2010年
2期
303-307
,共5页
严格偏序么半群%广义幂级数环%本质左理想%非奇异环
嚴格偏序麽半群%廣義冪級數環%本質左理想%非奇異環
엄격편서요반군%엄의멱급수배%본질좌이상%비기이배
strictly ordered monoid%ring of generalized power series%essential ideal%nonsingular ring
本文研究了广义幂级数环与其系数环在本质理想和非奇异性上的关系.利用本质理想的定义和性质,得到了广义幂级数环的左理想为本质左理想的菪干充分必要条件.在此基础上,给出了广义幂级数环为左非奇异环的充分必要条件.
本文研究瞭廣義冪級數環與其繫數環在本質理想和非奇異性上的關繫.利用本質理想的定義和性質,得到瞭廣義冪級數環的左理想為本質左理想的菪榦充分必要條件.在此基礎上,給齣瞭廣義冪級數環為左非奇異環的充分必要條件.
본문연구료엄의멱급수배여기계수배재본질이상화비기이성상적관계.이용본질이상적정의화성질,득도료엄의멱급수배적좌이상위본질좌이상적탕간충분필요조건.재차기출상,급출료엄의멱급수배위좌비기이배적충분필요조건.
In this article,we study the relations between generalized power series rings and their coefficient rings on essential ideal and nonsingularity. By using the definition and properties of essential ideal of rings, we show some necessary and sufficient conditions for a left ideal to be a left essential ideal, and provide several necessary and sufficient conditions for generalized power series rings to be a left nonsingular ring.
