Radically principal rings

[摘要] Let A be a commutative ring. An ideal I of A is radically principal if there exists a principal ideal J of A such that √ I = √ J. The ring A is radically principal if every ideal of A is radically principal. In this article, we study radically principal rings. We prove an analogue of the Cohen theorem, precisely, a ring is radically principal if and only if every prime ideal is radically principal. Also we characterize a zero-dimensional radically principal ring. Finally we give a characterization of polynomial ring to be radically principal.

[学科分类] 公共、环境与职业健康