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<p>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.</p>

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A-prime ideals and zeta functions over rings

  • 期刊论文

  • 发表日期：

    2026年2月23日

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  • Mustafa Alkan,
  • Nejma Ugljanin

摘要

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.