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The Splitting Problem for Coalgebras: A Direct Approach
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The Splitting Problem for Coalgebras: A Direct Approach

Miodrag-Cristian Iovanov
Applied Categorical Structures, Vol.14(5), pp.599-604
12/2006
DOI: 10.1007/s10485-006-9050-7

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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).
Mathematics Geometry splitting coalgebra 16W30 16Nxx 16S90 Theory of Computation 16Lxx torsion theory Convex and Discrete Geometry 18E40 Mathematical Logic and Foundations

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