The radical-annihilator monoid of a ring

Ryan C. Schwiebert
2016 Communications in Algebra  
Kuratowski's closure-complement problem gives rise to a monoid generated by the closure and complement operations. Consideration of this monoid yielded an interesting classification of topological spaces, and subsequent decades saw further exploration using other set operations. This article is an exploration of a natural analogue in ring theory: a monoid produced by "radical" and "annihilator" maps on the set of ideals of a ring. We succeed in characterizing semiprime rings and commutative
more » ... rings by their radical-annihilator monoids, and we determine the monoids for commutative local zero-dimensional (in the sense of Krull dimension) rings.
doi:10.1080/00927872.2016.1222401 fatcat:fipzvjie4bgephl2f6ay26fubu