Abstract
In this paper we introduce a generalization of direct families of algebras and we study their limits and sums. In the case of generalized direct families of algebras carried by idempotent algebras we investigate some subdirect decompositions of their sums. The results that we obtain generalize various results given by J.L. Chrislock and T. Tamura [2], M. Ciric and S. Bogdanovic [3-7], H. Mitsch [13], M. Petrich [14-16], B.M. Schein [23-24] and others.
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