Address: Universität Osnabrück, FB Mathematik/Informatik, 49069 Osnabrück, Germany
E-mail:
Peyman.Nasehpour@mathematik.uni-osnabrueck.de
Nasehpour@gmail.com
Abstract: In this article, we prove that in content extentions minimal primes extend to minimal primes and discuss zero-divisors of a content algebra over a ring who has Property (A) or whose set of zero-divisors is a finite union of prime ideals. We also examine the preservation of diameter of zero-divisor graph under content extensions.
AMSclassification: primary 13A15; secondary 13B25, 05C99.
Keywords: content algebra, few zero-divisors, McCoy’s property, minimal prime, property (A), primal ring, zero-divisor graph.