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The Splitting Problem for Coalgebras: A Direct Approach

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Abstract

In this note we give a new and elementary proof of a result of Năstăsescu and Torrecillas (J. Algebra, 281:144–149, 2004) stating that a coalgebra C is finite dimensional if and only if the rational part of any right module M over the dual algebra \(C^*\) is a direct summand in M (the splitting problem for coalgebras).

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Authors and Affiliations

  1. Faculty of Mathematics, University of Bucharest, Str. Academiei 14, RO-010014, Bucharest, Romania

    Miodrag-Cristian Iovanov

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  1. Miodrag-Cristian Iovanov
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Correspondence to Miodrag-Cristian Iovanov.

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Research supported by a CNCSIS BD-type grant, and by the bilateral project BWS04/04 “New Techniques in Hopf Algebra Theory and Graded Ring Theory” of the Flemish and Romanian governments.

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Iovanov, MC. The Splitting Problem for Coalgebras: A Direct Approach. Appl Categor Struct 14, 599–604 (2006). https://doi.org/10.1007/s10485-006-9050-7

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