We begin the investigation of the variety of semilattices of Mal?cev blocks, which we call SMB algebras.

In this paper we shall give another proof of a special case of Gao’s theorem for generating integrally indecomposable polygons in the sense of Minkowski. The approach of proving this theorem will enable us to give an effective algorithm for construction integrally indecomposable convex integral polygons with arbitrary many vertices. In such a way, classes of absolute irreducible bivariate polynomials corresponding to those indecomposable Newton polygons are generated.

The “semilattices of Mal’cev blocks”, for short SMB algebras, were defined by A. Bulatov. In a recently accepted paper by P. Đapić, P. Marković, R. McKenzie, and A. Prokić, the class of all SMB algebras and its subclass of regular SMB algebras were proved to be varieties of algebras. In this paper, we find an equational base of the first variety and simplify the previously known equational base of the second variety.