The Source of Primeness of Rings

Year 2022, Issue: 41, 100 - 104, 31.12.2022

Didem Yeşil , Didem Karalarlıoğlu Camcı

https://doi.org/10.53570/jnt.1189651

Cited By: 4

https://izlik.org/JA37YD59LB

Abstract

In this study, we define a new concept, i.e., source of primeness of a ring $R$, as $P_{R} := \bigcap_{a\in R} S_{R}^{a}$ such that $S_{R}^{a}:=\{b\in R \mid aRb=(0)\}$. 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.

Keywords

Prime ring , semiprime ring , source of primeness , source of semiprimeness

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