On right S-Noetherian rings and S-Noetherian modules - TEKİR, ÜNSAL (TAYLOR & FRANCIS INC, 2018)
In this paper we study right S-Noetherian rings and modules, extending notions introduced by Anderson and Dumitrescu in commutative algebra to noncommutative rings. Two characterizations of right S-Noetherian rings are given in terms of completely prime right ideals and point annihilator sets. We also prove an existence result for completely prime point annihilators of certain S-Noetherian modules with the following consequence in commutative algebra: If a module M over a commutative ring is S-Noetherian with respect to a multiplicative set S that contains no zero-divisors for M, then M has an associated prime.
Keywords: Completely prime right ideals; Oka families of right ideals; point annihilator sets; right S-Noetherian rings; PRIME IDEAL PRINCIPLE