3 citations · 9 across the 30 of their papers we have counts for
5 papers · 1 filter
Structural results on harmonic rings and lessened rings
Abolfazl Tarizadeh, Mohsen Aghajani
In this paper, a combination of algebraic and topological methods are applied to obtain new and structural results on harmonic rings. Especially, it is shown that if a Gelfand ring…
Avoidance and Absorbance
Abolfazl Tarizadeh, Justin Chen
We study the two dual notions of prime avoidance and prime absorbance. We generalize the classical prime avoidance lemma to radical ideals. A number of new criteria are provided fo…
Some results on pure ideals and trace ideals of projective modules
Abolfazl Tarizadeh
Let be a commutative ring with the unit element. It is shown that an ideal in is pure if and only if Ann for all . If is the trace of a projective…
Structure theory of p.p. rings and their generalizations
Abolfazl Tarizadeh
In this paper, new and significant advances on the understanding the structure of p.p. rings and their generalizations have been made. Especially among them, it is proved that a co…
On purely-prime ideals with applications
Abolfazl Tarizadeh, Mohsen Aghajani
In this paper, new algebraic and topological results on purely-prime ideals of a commutative ring (pure spectrum) are obtained. Especially, Grothendieck type theorem is obtained wh…