( L , ϕ ) -representations of algebras

Andrzej Walendziak

Archivum Mathematicum (1993)

  • Volume: 029, Issue: 3-4, page 135-143
  • ISSN: 0044-8753

Abstract

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In this paper we introduce the concept of an ( L , ϕ ) -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.

How to cite

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Walendziak, Andrzej. "$(L,\varphi )$-representations of algebras." Archivum Mathematicum 029.3-4 (1993): 135-143. <http://eudml.org/doc/247426>.

@article{Walendziak1993,
abstract = {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.},
author = {Walendziak, Andrzej},
journal = {Archivum Mathematicum},
keywords = {finitely restricted subdirect product; full subdirect product; weak direct product; congruence lattice; distributivity; full subdirect; weak direct; representations; congruence relations},
language = {eng},
number = {3-4},
pages = {135-143},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {$(L,\varphi )$-representations of algebras},
url = {http://eudml.org/doc/247426},
volume = {029},
year = {1993},
}

TY - JOUR
AU - Walendziak, Andrzej
TI - $(L,\varphi )$-representations of algebras
JO - Archivum Mathematicum
PY - 1993
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 029
IS - 3-4
SP - 135
EP - 143
AB - 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.
LA - eng
KW - finitely restricted subdirect product; full subdirect product; weak direct product; congruence lattice; distributivity; full subdirect; weak direct; representations; congruence relations
UR - http://eudml.org/doc/247426
ER -

References

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  1. Algebraic theory of lattices, Prentice-Hall, Englewood Cliffs (N.J.), 1973. (1973) 
  2. Weak direct product decomposition of algebras, In: Contributions to General Algebra 5, Proc. of the Salzburg Conference (1986), Wien (1987), 105-121. MR0930914
  3. Direct, subdirect decompositions and congruence relations, Osaka Math. J. 9 (1957), 87-112. (1957) Zbl0078.01805MR0091248
  4. Weak product decompositions of discrete lattices, Czech Math. J. 21(96) (1971), 399-412. (1971) MR0286723
  5. Algebras, Lattices, Varieties, Volume I, California, Monterey, 1987. MR0883644

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