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Ideal extensions of graph algebras
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 933-947 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $\mathcal A$ and $\mathcal B$ be graph algebras. In this paper we present the notion of an ideal in a graph algebra and prove that an ideal extension of $\mathcal A$ by $\mathcal B$ always exists. We describe (up to isomorphism) all such extensions.
Let $\mathcal A$ and $\mathcal B$ be graph algebras. In this paper we present the notion of an ideal in a graph algebra and prove that an ideal extension of $\mathcal A$ by $\mathcal B$ always exists. We describe (up to isomorphism) all such extensions.
Classification : 08A30
Keywords: oriented graph; graph (Shallon) algebra; congruence relation; ideal; quotient graph algebra; ideal extension 
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Čipková, Karla. Ideal extensions of graph algebras. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 933-947. http://geodesic.mathdoc.fr/item/CMJ_2006_56_3_a11/

[1] A. H. Clifford: Extension of semigroup. Trans. Amer. Math. Soc. 68 (1950), 165–173. | DOI | MR

[2] A. J. Hullin: Extension of ordered semigroup. Czechoslovak Math. J. 26(101) (1976), 1–12.

[3] D. Jakubíková-Studenovská: Subalgebra extensions of partial monounary algebras. Czechoslovak Math. J, Submitted. | MR

[4] N. Kehaypulu, P. Kiriakuli: The ideal extension of lattices. Simon Stevin 64, 51–56. | MR

[5] N. Kehaypulu, M. Tsingelis: The ideal extension of ordered semigroups. Commun. Algebra 31 (2003), 4939–4969. | DOI | MR

[6] E. W. Kiss, R. Pöschel, P. Pröhle: Subvarieties of varieties generated by graph algebras. Acta Sci. Math. 54 (1990), 57–75. | MR

[7] J. Martinez: Torsion theory of lattice ordered groups. Czechoslovak Math. J. 25(100) (1975), 284–299. | MR

[8] S. Oates-Macdonald, M. Vaughan-Lee: Varieties that make one cross. J. Austral. Math. Soc. (Ser. A) 26 (1978), 368–382. | DOI | MR

[9] S. Oates-Williams: On the variety generated by Murskii’s algebra. Algebra Universalis 18 (1984), 175–177. | DOI | MR | Zbl

[10] R. Pöschel: Graph algebras and graph varieties. Algebra Universalis 27 (1990), 559–577. | DOI | MR

[11] R. Pöschel: Shallon algebras and varieties for graphs and relational systems. Algebra und Graphentheorie (Jahrestagung Algebra und Grenzgebiete), Bergakademie Freiberg, Section Math., Siebenlehn, 1986, pp. 53–56.

[12] C. R. Shallon: Nonfinitely based finite algebras derived from lattices. PhD.  Dissertation, U.C.L.A, 1979.