Yazar "Molina, Mercedes Siles" seçeneğine göre listele

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    Basic ideals in evolution algebras
    (Elsevier Science Inc, 2019) Casado, Yolanda Cabrera; Er, Müge Kanuni; Molina, Mercedes Siles
    With the aim of finding useful tools and invariants to classify finite dimensional evolution algebras, we introduce and study the notion of a basic ideal. Every n-dimensional perfect evolution algebra has a maximal basic ideal I which is unique except when the dimension of I is n-1. An application of our results leads to the description of the four dimensional perfect non-simple evolution algebras over a field with mild restrictions. (C) 2019 Elsevier Inc. All rights reserved.
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    CLASSIFICATION OF LEAVITT PATH ALGEBRAS WITH TWO VERTICES
    (Independent Univ Moscow-Ium, 2019) Kanuni, Müge; Barquero, Dolores Martin; Gonzalez, Candido Martin; Molina, Mercedes Siles
    We classify row-finite Leavitt path algebras associated to graphs with no more than two vertices. For the discussion we use the following invariants: decomposability, the K-0 group, det(N-E') (included in the Franks invariants), the type, as well as the socle, the ideal generated by the vertices in cycles with no exits and the ideal generated by vertices in extreme cycles. The starting point is a simple linear algebraic result that determines when a Leavitt path algebra is IBN. An interesting result that we have found is that the ideal generated by extreme cycles is invariant under any isomorphism (for Leavitt path algebras whose associated graph is finite). We also give a more specific proof of the fact that the shift move produces an isomorphism when applied to any row-finite graph, independently of the field we are considering.