The Source of Primeness of Rings

Authors : Didem YEŞİL, Didem KARALARLIOĞLU CAMCI

Pages : 100-104

Doi:10.53570/jnt.1189651

View : 20 | Download : 10

Publication Date : 2022-12-31

Article Type : Research Paper

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 $S_{R}^{a}:=\\{b\\in R \\mid aRb=insert ignore into journalissuearticles values(0);\\}$. 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