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PROPERTIES OF K-RINGS AND RINGS SATISFYING SIMILAR CONDITIONS
https://doi.org/10.1142/S0218196711006613Cited by:3 (Source: Crossref)
Abstract
Jacobson introduced the concept of K-rings, continuing the investigation of Kaplansky and Herstein into the commutativity of rings. In this note we focus on the ring-theoretic properties of K-rings. We first construct basic examples of K-rings to be handled easily. It is shown that a semiprime K-ring of bounded index of nilpotency is a commutative domain. It is proved that if R is a prime K-ring then its classical quotient ring is a local ring with a nil Jacobson radical. We also show that if R is a π-regular K-ring then R/P is a field for every strongly prime ideal P of R. The basic structure of a condition, unifying K-rings and reversible rings, is studied with respect to zero-divisors in matrices and polynomials.
AMSC: 16U80, 16N40, 16N60, 16E50, 16S36
