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Keywords:
oriented graph; graph (Shallon) algebra; congruence relation; ideal; quotient graph algebra; ideal extension
oriented graph; graph (Shallon) algebra; congruence relation; ideal; quotient graph algebra; ideal extension
Summary:
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.
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