The Source of Primeness of Rings
Authors : Didem Yeşil, Didem Karalarlioğlu Camci
Pages : 100-104
Doi:10.53570/jnt.1189651
View : 11 | Download : 6
Publication Date : 2022-12-31
Article Type : Research
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