A taxonomy of 2-primal rings

By G. Marks. 2003

92 citations recorded by the source corpus.

Abstract Various conditions on a noncommutative ring imply that it is 2-primal (i.e., the ring's prime radical coincides with the set of nilpotent elements of the ring). We will examine several such conditions and show that their known interdependencies are their only ones. Of particular interest will be the (PS I) condition on a ring (i.e., every factor ring modulo the right annihilator of a principal right ideal is 2-primal). We will see that even within a fairly narrow class of rings, (PS I) is a strictly stronger condition than 2-primal. We will show that the (PS I) condition is left-right asymmetric. We will also study the interplay between various types of semilocal rings and various types of 2-primal rings. The Kothe Conjecture will make a cameo appearance. In Section 6, we will examine subideals of prime ideals of commutative rings that are invariant under derivations.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a46cf810f6d27e29d3ac869e88a15984a9d2f36b

Citations in the corpus

• A UNIFIED APPROACH TO VARIOUS GENERALIZATIONS OF ARMENDARIZ RINGS (2010, unknown): “There is a substantial literature on these conditions, a survey of some of which can be found in [28].”