Research Information System
Journal of New Theory, no.41, pp.100-104, 2022 (Peer-Reviewed Journal)
In this study, we define a new concept, i.e., source of primeness of a ring $R$, as $P_{R} := bigcap_{ain R} S_{R}^{a}$ such that $S_{R}^{a}:={bin R mid aRb=(0)}$. We then examine some basic properties of $P_{R}$ related to the ring’s idempotent elements, nilpotent elements, zero divisor elements, and identity elements. Finally, we discuss the need for further research.