Subdirectly irreducible generalized sums of upper semilattice ordered systems of algebras. (Q1771912)

The concept of a generalized sum of an upper \((F_1,F_2)\)-semilattice system of algebras was introduced by \textit{A. Wojtunik} [Demonstr. Math. 24, 129--147 (1991; Zbl 0785.08004)]. The authors find necessary and sufficient conditions under which this construction yields subdirectly irreducible algebras. The result is applied for varieties of bisemilattices, certain generalizations of Boolean algebras, groups, Abelian groups and rings.