Department of Mathematics, Pachaiyappa’s College, Chennai – 600 030 (India)

In this paper for the first time groupoid matrix semirings are introduced and their properties are analysed. A matrix groupoid or a groupoid matrix is a collection of p × q matrices with entries from a groupoid (G, *) where groupoid matrix inherits the operation of G. Here chain lattices are used as semirings and groupoid matrix semirings are non associative semirings of finite order, as both the groupoids G and the chain lattices are of finite order.