Journal article
The generating condition for coalgebras
Bulletin of the London Mathematical Society, Vol.41(3), pp.483-494
2009
DOI: 10.1112/blms/bdp020
Abstract
For a ring R , the properties of being (left) self‐injective or being a cogenerator for the left R ‐modules do not imply one another, and the two combined give rise to the important notion of pseudo‐Frobenius‐rings. For a coalgebra C , (left) self‐projectivity implies that C is a generator for right comodules and the coalgebras with this property are called right quasi‐co‐Frobenius; however, whether the converse implication is true is an open question. We provide an extensive study of this problem. We show that this implication does not hold, by giving a large class of examples of coalgebras having the ‘generating property’. In fact, we show that any coalgebra C can be embedded in a coalgebra C ∞ that generates its right comodules, and, if C is local over an algebraically closed field, then C ∞ can be chosen local as well. We also give some general conditions under which the implication ‘ C ‐projective (left) ⇒ C generator for right comodules’ does work, and such conditions are when C is right semiperfect or when C has finite coradical filtration.
Details
- Title: Subtitle
- The generating condition for coalgebras
- Creators
- Miodrag Cristian Iovanov
- Resource Type
- Journal article
- Publication Details
- Bulletin of the London Mathematical Society, Vol.41(3), pp.483-494
- DOI
- 10.1112/blms/bdp020
- ISSN
- 1469-2120
- eISSN
- 1469-2120
- Language
- English
- Date published
- 2009
- Academic Unit
- Mathematics
- Record Identifier
- 9983985838502771
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