2024/01/16 by Nongsiej, Raplang, Buhphang, Ardeline Mary
#16D10 #16D40 #16D60 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2401.08535
The class of nil-essential ideals is a generalisation of the class of essential ideals. Every nil-essential ideal of a reduced ring is essential. Therefore the intersection of all nil-essential ideals over a reduced ring R is the socle of R. In this note, we apply this generalisation to give a new criteria of semisimplicity in terms of nil-essentiality of ideals.