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On Sums of Compositions of Irreducible Morphisms

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Abstract

We consider A an artin algebra. We study the relationship between sums of compositions of irreducible morphisms and the powers of the radical of their module category.

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References

  1. Bautista, R.: On irreducible maps. Bull. Am. Math. Soc. N.S(2), 177–180 (1980)

    Article  MathSciNet  Google Scholar 

  2. Butler, M., Ringel, C.: Auslander-reiten sequences with few middle terms and applications to string algebras. Commun. Algebra 15(1), 145–179 (1987)

    Article  MathSciNet  Google Scholar 

  3. Castonguay, D., Dionne, J., Huard, F., Lanzilotta, M.A.: Toupie algebras, some examples of Laura algebras. arXiv:1011.5136v1 (2010)

  4. Chaio, C.: Degrees and composite of irreducible morphisms in almost pre-sectional paths. Algebr. Represent. Theory 17(2), 407–432 (2014)

    Article  MathSciNet  Google Scholar 

  5. Chaio, C.: Degrees in Auslander-Reiten components with almost split sequences of at most two middle terms. J. Algebra Its Appl. 14(7) (2015)

    Article  MathSciNet  Google Scholar 

  6. Chaio, C.: A generalization of the composition of irreducible morphisms in regular components. Algebr. Represent. Theory 18(2), 323–337 (2015)

    Article  MathSciNet  Google Scholar 

  7. Chaio, C.: On the compositions of irreducible morphisms. Actas del XIII Congreso Dr. Antonio Monteiro 2015, 27–38 (2016)

    MathSciNet  MATH  Google Scholar 

  8. Chaio, C., Coelho, F.U., Trepode, S.: On the composite of two irreducible morphisms in radical cube. J. Algebra 312, 650–667 (2007)

    Article  MathSciNet  Google Scholar 

  9. Chaio, C., Coelho, F.U., Trepode, S.: On the composite of three irreducible morphisms in the fourth power of the radical. Commun. Algebra 39(2), 555–559 (2011)

    Article  MathSciNet  Google Scholar 

  10. Chaio, C., Le Meur, P., Trepode, S.: Degrees of irreducible morphisms and finite-representation type. J. London Math. Soc. II 84(1), 35–57 (2011)

    Article  MathSciNet  Google Scholar 

  11. Chaio, C., Le Meur, P., Trepode, S.: Covering techniques in Auslander-Reiten theory. To appear in Journal of Pure and Applied Algebras. arXiv:1412.0188 (2014)

  12. Chaio, C., Llodra Schat, N.: A characterization of the irreducible morphisms of degree three. To appear in Communications in Algebra (2017)

  13. Chaio, C., Malicki, P.: Composition of irreducible morphisms in quasi-tubes. J. Algebra Appl. 16(4), 1750071 (2017). 24

    Article  MathSciNet  Google Scholar 

  14. Chaio, C., Platzeck, M.I., Trepode, S.: On the degree of irreducible morphisms. J. Algebra 281(1), 200–224 (2004)

    Article  MathSciNet  Google Scholar 

  15. Igusa, K., Todorov, G.: A characterization of finite Auslander-Reiten quivers. J. Algebra 89, 148–177 (1984)

    Article  MathSciNet  Google Scholar 

  16. Liu, S.: Degree of irreducible maps and the shapes of Auslander-Reiten quivers. J. Lond. Math. Soc. 2(45), 32–54 (1992)

    Article  MathSciNet  Google Scholar 

  17. Liu, S.: Shapes of connected components of the auslander-reiten quivers of artin algebras. Proc. Am. Math. Soc. CMS Conf. 19, 109–137 (1996)

    MathSciNet  MATH  Google Scholar 

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Acknowledgments

The authors thankfully acknowledge partial support from CONICET and from Universidad Nacional de Mar del Plata, Argentina. The first author is a researcher from CONICET.

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Correspondence to Claudia Chaio.

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Presented by: Jon F. Carlson

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Chaio, C., Llodra Schat, N. On Sums of Compositions of Irreducible Morphisms. Algebr Represent Theor 23, 67–93 (2020). https://doi.org/10.1007/s10468-018-9838-9

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  • DOI: https://doi.org/10.1007/s10468-018-9838-9

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