Semigroup Forum https://doi.org/10.1007/s00233-018-9983-9 RESEARCH ARTICLE A note on additively completely regular seminearrings Rajlaxmi Mukherjee 1 · Tuhin Manna 2 · Pavel Pal 3 Received: 8 August 2018 / Accepted: 3 November 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In the endeavour of obtaining semigroup theoretic analogues i.e., the analogues of structure theorems of completely regular semigroups in the setting of additively regu- lar seminearrings we could obtain some results in Mukherjee et al. (Commun Algebra 45(12):5111–5122, 2017). But we could not obtain the analogue of (i ) ‘A semigroup is Clifford if and only if it is strong semilattice of groups’ and (ii ) ‘ A semigroup is completely regular if and only if it is a union of groups’. In Mukherjee et al. (Commun Algebra, https://doi.org/10.1080/00927872.2018.1524011) we could obtain the ana- logue of (i ) for some restricted type of left (right) Clifford seminearrings. The main purpose of this paper is to complete the remaining task i.e., to obtain the analogue of (ii ) for a class of additively completely regular seminearrings. In order to accomplish this we have characterized those seminearrings which are union of near-rings (zero- symmetric near-rings) in the class of additively completely regular seminearrings. Keywords Left (right) completely regular seminearring · Generalized left (right) completely regular seminearring · Union of near-rings (zero-symmetric near-rings) Communicated by Lev N. Shevrin. B Rajlaxmi Mukherjee ju.rajlaxmi@gmail.com Tuhin Manna iamtuhinmanna@gmail.com Pavel Pal ju.pavel86@gmail.com 1 Department of Mathematics, Garhbeta College, Paschim Medinipur 721127, India 2 Department of Mathematics, Jadavpur University, Kolkata 700032, India 3 Department of Mathematics, Bankura University, Bankura 722155, India 123