On the sum of a direct system of universal algebras with nullary polynomials
In the presence of nullary operations, the sum of a direct system of universal algebras in the sense of the author's earlier paper [Fundam. Math. 61, 183-189 (1967; Zbl 0168.267)] can be formed when the direct system contains a smallest member. Various theorems from the above and another paper of the author [ibid. 64, 241-247 (1969; Zbl 0187.287)] remain valid for the extended sum concept, e.g.: An equation holds in a nontrivial sum iff it is regular and holds in each summand. If K is an equational class such that an equation of the form \(x\cdot y=x\) holds in K, then any algebra satisfying all regular equations that hold in K is the sum of a direct system of algebras from K.
scientific article; zbMATH DE number 3873398