On full subdirect products of a bi-semilattice and a (zero-symmetric) near-ring

Abstract

In order to find an analogue of the structure theorem,“a semigroup is a full subdirect product of a semilattice and a group if and only if it is an [Formula: see text]-inversive sturdy semilattice of cancellative monoids (Theorem 14 of [H. Mitsch, Subdirect products of E-inversive semigroups, J. Austral. Math. Soc. 48 (1990) 66–78])”, in the setting of seminearrings we have characterized the seminearrings which are full subdirect products of a bi-semilattice and a (zero-symmetric) near-ring and which are subdirect products of a distributive lattice and a (zero-symmetric) near-ring.