Integrality and Jacobson Radicals of Finite Normalizing Extension Rings

Abstract

본 논문에서는 유한정규 확장환에 있어 몇가지 성질을 다루도록 하겠다. Martin Lorenz와 D.S. Passman에 의해 소개되어진 환에 있어서의 Integrality 성질을 보다 일반화 시키고 그 결과를 이용해 R의 Jacobson Radical J(R)과 S의 Jacobson Radical J(S)사이의 관계가 J(R)=J(S)∩R이라는 것을 보여주겠다.

In this paper we consider finite normalizing extension rings. We will generalize the integrality results which are introduced by Martin Lorenz. Using this results we show that the Jacobson Radicals of R and S are related by J(S)∩R where S is a finite normalizing extension ring of R.

In this paper we consider finite normalizing extension rings. We will generalize the integrality results which are introduced by Martin Lorenz. Using this results we show that the Jacobson Radicals of R and S are related by J(S)∩R where S is a finite normalizing extension ring of R.