Abstract
Keigher showed that quasi‐prime ideals in differential commutative rings are analogues of prime ideals in commutative rings. In that direction, he introduced and studied new types of differential rings using quasi‐prime ideals of a differential ring. In the same sprit, we define and study two new types of differential rings which lead to the mirrors of the corresponding results on von Neumann regular rings and principally flat rings (PF‐rings) in commutative rings, especially, for rings of positive characteristic.
Highlights
The derivatives of rings play important roles in ring theory
A ring R is called a PF-ring if every principal ideal aR of R is an R-flat module
3 If R is von Neumann regular ring and I is an ideal of R, R/I is von Neumann regular
Summary
The derivatives of rings play important roles in ring theory. In particular, they are used to define various ring constructions, for example, see Sections 3.4 to 3.7 of the monograph 1. Recall that an ideal I in a ring R is called a pure ideal if, for each a ∈ I, there exists b ∈ I such that ab a. A quasiprime ideal of a differential ring is a generalization of a prime ideal of a ring R. In Keigher 10, 11 , the differential rings constructed from quasiprime ideals via quotient rings and rings of fractions were studied too. We define two new types of differential rings that can be constructed using quasiprime ideals. A differential ring R, δ is said to be quasiregular if R is quasireduced and every quasiprime ideal is quasimaximal. A differential ring R, δ is called a quasi-PF ring if R is quasireduced and every quasiprime ideal of it contains a unique minimal quasiprime ideal. We investigate when the Hurwitz series ring is quasiregular or quasi-PF, in particular, for rings of positive characteristic
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
