WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS

Year 2020, , 43 - 60, 14.07.2020

Nico Groenewald

https://doi.org/10.24330/ieja.768127

Cited By: 5

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

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