On Sturdy Frame of Abstract Algebras

Yong Shao, Miaomiao Ren

We introduce the notion of a sturdy frame of abstract algebras which is a common generalization of a sturdy semilattice of semigroups, the sum of lattice ordered systems, the strong distributive lattice of semirings, the sturdy frame of type $(2,2)$ algebras and the strong b-lattice of semirings. Also, we give some properties and characterizations of the sturdy frame of abstract algebras. As an application, we study the sturdy distributive lattice of lattice ordered groups.