Abstract: In this paper, we studied semirings in which additive semigroups were semilattices, multiplicative semigroups were nil extensions of rectangular groups. From the subsets of semirings, the relations on multiplicative semigroups were constructed. The necessary and sufficient condition for H- to be the congruence relation on semirings (Reg(S),+,·) was obtained. The conditions under which nil extension of a rectangular group could be transformed into nil extension of a rectangular band were given. The property of nil extension of rectangular groups was extended to the nil extension of rectangular bands and rectangular groups.

Key words: semirings, rectangular groups, GV semigroups, congruence, nil extensions