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Article

Walendziak, Andrzej
$(L,\varphi)$-representations of algebras. (English). Archivum Mathematicum, vol. 29 (1993), issue 2, pp. 135-143
MSC: 08A05, 08A30, 08B26 | MR 1263114 | Zbl 0796.08002
Keywords:
finitely restricted subdirect product; full subdirect product; weak direct product; congruence lattice; distributivity
Summary:
In this paper we introduce the concept of an $(L, \varphi )$-representation of an algebra $A$ which is a common generalization of subdirect, full subdirect and weak direct representation of $A$. Here we characterize such representations in terms of congruence relations.
References:
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[3] Hashimoto, J.: Direct, subdirect decompositions and congruence relations. Osaka Math. J. 9 (1957), 87-112. MR 0091248 | Zbl 0078.01805
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[5] McKenzie, R., McNulty, G., Taylor, W.: Algebras, Lattices, Varieties. Volume I, California, Monterey, 1987. MR 0883644
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