Title of article :
WEAKLY PRIME and WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS
Author/Authors :
Groenewald, Nico Department of Mathematics and Applied Mathematics - Nelson Mandela University - Port Elizabeth, South Africa
Abstract :
Anderson-Smith studied weakly prime ideals for a commutative
ring with identity. Hirano, Poon and Tsutsui studied the structure of a ring
in which every ideal is weakly prime for rings, not necessarily commutative.
In this note we give some more properties of weakly prime ideals in noncommutative rings. We introduce the notion of a weakly prime radical of an ideal.
We initiate the study of weakly completely prime ideals and investigate rings
for which every proper ideal is weakly completely prime
Keywords :
Weakly prime ideal , weakly prime radical , weakly completely prime ideal
Journal title :
International Electronic Journal of Algebra
