Structure of unit-IFP rings
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In this article we first investigate a sort of unit-IFP ring by which Antoine provides very useful information to ring theory in relation with the structure of coefficients of zero-dividing polynomials. Here we are concerned with the whole shape of units and nilpotent elements in such rings. Next we study the properties of unit-IFP rings through group actions of units on nonzero nilpotent elements. We prove that if $R$ is a unit-IFP ring such that there are finite number of orbits under the left (resp., right) action of units on nonzero nilpotent elements, then $R$ satisfies the descending chain condition for nil left (resp., right) ideals of $R$ and the upper nilradical of $R$ is nilpotent.
Abstract
In this article we first investigate a sort of unit-IFP ring by which Antoine provides very useful information to ring theory in relation with the structure of coefficients of zero-dividing polynomials. Here we are concerned with the whole shape of units and nilpotent elements in such rings. Next we study the properties of unit-IFP rings through group actions of units on nonzero nilpotent elements. We prove that if $R$ is a unit-IFP ring such that there are finite number of orbits under the left (resp., right) action of units on nonzero nilpotent elements, then $R$ satisfies the descending chain condition for nil left (resp., right) ideals of $R$ and the upper nilradical of $R$ is nilpotent.
참고문헌 (9)
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