ENDOMORPHISM RINGS OF MODULES OVER PRIME RINGS

Abstract

Endomorphism rings of modules appear as the center of a ring, as the fix ring of a ring with group action or as the subring of constants of a derivation. This note discusses the question whether certain $*$-prime modules have a prime endomorphism ring. Several conditions are presented that guarantee the primeness of the endomorphism ring. The contours of a possible example of a $*$-prime module whose endomorphism ring is not prime are traced.