ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 68, 1 (1999)
pp. 91-110

STRICT REFINEMENT FOR DIRECT SUMS AND GRAPHS
A. A. ISKANDER

Abstract. We study direct sums of structures with a one element subuniverse. We give a characterization of direct sums reminescent to that of inner products of groups. The strict refinement property is adapted to direct sums and to restricted Cartesian products of graphs. If a structure has the strict refinement property (for direct products), it has the strict refinement property for direct sums. Connected graphs satisfy the strict refinement property for their restricted Cartesian products.

AMS subject classification. 05C99, 08B25; Secondary 68R10
Keywords. Direct sums, algebras with a one element subuniverse, direct sum sets, dual direct sum sets of congruences, graphs, vertex, edge, homomorphism, Cartesian product, strict refinement property, refinement property, direct factor sets, Cartesian indecomposable graphs, connected graphs, unique factorization

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Acta Mathematica Universitatis Comenianae
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Comenius University
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