A-prime ideals and zeta functions over rings

ALKAN M., Ugljanin N.

Acta Universitatis Sapientiae, Mathematica, cilt.18, sa.1, 2026 (ESCI, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 1
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1007/s44426-026-00031-5
  • Dergi Adı: Acta Universitatis Sapientiae, Mathematica
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: Absorbing ideals, Prime ideals, S-prime ideals, Weakly prime ideals, Zeta functions of rings
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.