Geodesic
Almost prime ideals in noncommutative rings
Serdica Mathematical Journal, Tome 48 (2022) no. 4, pp. 235-246.

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A proper ideal \(P\) of a commutative ring with identity is an almost prime ideal if \(ab \in P{\setminus}P^2\) implies \(a \in P\) or \(b \in P\). In this paper we define almost prime ideals of a noncommutative ring, and provide some equivalent definitions. We also examine some cases such that all right ideals of a noncommutative ring are almost prime right ideals.
Keywords: 13A15, 17A01 
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Abouhalaka, Alaa; Fındık, Şehmus. Almost prime ideals in noncommutative rings. Serdica Mathematical Journal, Tome 48 (2022) no. 4, pp. 235-246. http://geodesic.mathdoc.fr/item/SMJ2_2022_48_4_a2/