Research Information System
Amesia, vol.6, no.2, pp.113-121, 2025 (Peer-Reviewed Journal)
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.