Structural Characterizations of Primeness in Semigroups

Yeşil D., Mekera R.

Amesia, cilt.6, sa.2, ss.113-121, 2025 (Hakemli Dergi)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 6 Sayı: 2
  • Basım Tarihi: 2025
  • Doi Numarası: 10.54559/amesia.1759955
  • Dergi Adı: Amesia
  • Sayfa Sayıları: ss.113-121
  • Çanakkale Onsekiz Mart Üniversitesi Adresli: Evet

Özet

This study investigates the set PS = {b ∈ S | SSb = (0)} for a semigroup S with zero, where PS is referred to as the source of primeness of S. The paper first explores the fundamental algebraic properties of PS, establishing its structural role within the semigroup. It then provides a characterization of |PS|-regular, |PS|-idempotent, |PS|-reduced, and |PS|- nonzero-divisor semigroups. Furthermore, the work considers the relationship between the notions of semiprimeness and primeness in semigroups, highlighting how the source of primeness can serve as a tool to analyze and distinguish these concepts. An illustrative example is presented to demonstrate the applicability of the results.