On additively completely regular seminearrings
Rajlaxmi Mukherjee, Pavel Pal, Sujit Kumar Sardar · Communications in Algebra · 2017
In an attempt to investigate the situation arising out of replacing additive regularity by additive complete regularity in our previous study on additively regular seminearrings, we introduce the notions of left (right) completely regular seminearrings and characterize left (right) completely regular seminearrings as bi-semilattices of left (resp., right) completely simple seminearrings. We also define left (right) Clifford seminearrings and show that they are precisely bi-semilattices of near-rings (resp., zero-symmetric near-rings).