Serial coalgebras and their valued Gabriel quivers

Gómez-Torrecillas, José; Navarro, Gabriel

doi:10.1016/j.jalgebra.2008.03.020

Cited by 9 publications

(15 citation statements)

References 26 publications

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“…From Proposition 3.3 and the corresponding conclusion in [5], we conjecture that the coalgebra C is right (resp. left) m ( * )-serial if the localized coalgebra eCe is right (resp.…”

Section: Lemma 23 [23]mentioning

confidence: 83%

“…Since a ( * )-serial coalgebra is more complicated than serial one, the conditions here are stronger than the corresponding ones in [5]. Meanwhile, the proof here is also harder and longer than one there.…”

Section: Lemma 23 [23]mentioning

confidence: 87%

“…Lemma 2.7 [5] Let C be a coalgebra, and let e be an idempotent in C * . Then the following statements hold.…”

Section: Lemma 23 [23]mentioning

confidence: 99%

“…In Section 2, we list some notations and basic facts about coalgebras, localization and quivers, in order to make the article self-contained. In Section 3, we characterize the localization in right ( * )-serial coalgebras, which is motivated by [5], and obtain some results similar to (but with different proofs) those in [5].…”

Section: Introductionmentioning

confidence: 95%

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Localization in right (*)-serial coalgebras

Fan

Yao

2010

Front. Math. China

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“…From Proposition 3.3 and the corresponding conclusion in [5], we conjecture that the coalgebra C is right (resp. left) m ( * )-serial if the localized coalgebra eCe is right (resp.…”

Section: Lemma 23 [23]mentioning

confidence: 83%

Section: Lemma 23 [23]mentioning

confidence: 87%

“…Lemma 2.7 [5] Let C be a coalgebra, and let e be an idempotent in C * . Then the following statements hold.…”

Section: Lemma 23 [23]mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

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Localization in right (*)-serial coalgebras

Fan

Yao

2010

Front. Math. China

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“…We recall a few definitions used in [C,CGT04,GN,IO,LS]; the terminology is derived from serial modules. Given a coalgebra C, a C-comodule M is called uniserial if M has a unique composition series, equivalently, the lattice of submodules of M is totally ordered.…”

Section: E(s) N(s) As Left C-comodules Where E(s) Is An Injective Humentioning

confidence: 99%

Triangular matrix coalgebras and applications

Iovanov

2013

Linear and Multilinear Algebra

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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 C is a coalgebra such that the rational part of every left finitely generated C * -module splits off if and only if C = D M 0 E is an upper triangular matrix coalgebra, for a serial coalgebra D whose Ext-quiver is a finite union of cycles, a finite dimensional coalgebra E and a finite dimensional bicomodule M .

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