In this paper, we introduce the concept of an A-prime ideal as a structural generalization of prime ideals in a commutative ring with identity. Then we study the behavior of A-prime ideals and give the characterization of this new class in some ring class. Moreover, we investigate the connection between these generalizations and the zeta function of a ring, similar to the form of an Euler product.
Alkan et al. (Mon,) studied this question.
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