Journal article
Triangular matrix coalgebras and applications
Linear and Multilinear Algebra, Vol.63(1), pp.46-67
01/02/2015
DOI: 10.1080/03081087.2013.844233
Abstract
We formally introduce and study generalized comatrix coalgebras and upper triangular comatrix coalgebras, which are not only a dualization but also an extension of classical generalized matrix algebras. We use these to answer several open questions on Noetherian and Artinian type notions in the theory of coalgebras, and to give complete connections between these. We also solve completely the so called finite splitting problem for coalgebras: we show that is a coalgebra such that the rational part of every left finitely generated -module splits off if and only if is an upper triangular matrix coalgebra, for a serial coalgebra whose Ext-quiver is a finite union of cycles, a finite dimensional coalgebra and a finite dimensional bicomodule .
Details
- Title: Subtitle
- Triangular matrix coalgebras and applications
- Creators
- Miodrag Cristian Iovanov - Faculty of Mathematics, University of Bucharest
- Resource Type
- Journal article
- Publication Details
- Linear and Multilinear Algebra, Vol.63(1), pp.46-67
- DOI
- 10.1080/03081087.2013.844233
- ISSN
- 0308-1087
- eISSN
- 1563-5139
- Publisher
- Taylor & Francis
- Language
- English
- Date published
- 01/02/2015
- Academic Unit
- Mathematics
- Record Identifier
- 9983985961202771
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