Our purpose in these notes is to present a result for a specific Nakayama Algebra. In essence, it affirms that for any order of simple modules, the cyclic Nakayama Algebras with relations (i.e. ) are not standardly stratified or costandardly stratified.
References
[1]
Nakayama, T. (1940) Note on Uni-serial and Generalized Uni-serial Rings. Mathematical Institute, Osaka Imperial University, Japanese, 285-289.
[2]
Ringel, C.M. (1991) The Category of Modules with Good Filtrations over a Quasi-Hereditary Algebras Has Almost Split Sequences. Mathematische Zeitschrift, 208, 209-223.
[3]
Xi, C.C. (2002) Standardly Stratified Algebras and Cellular Algebras. Mathematical Proceedings of the Cambridge Philosophical Society, 133, 37-53.
[4]
Dlab, V. (1994) Quasi-hereditary Algebras. Appendix Finite Dimensional Algebras by Drozd, Y. and Kirichenko, V., Springer-Verlag, 213-244.
[5]
Dlab, V. and Ringel, C.M. (1998) Quasi-Hereditary Algebras. Carleton Mathematical Series, 224.
[6]
Dlab, V. and Ringel, C.M. (1991) Auslander Algebras as Quasi-Hereditary Agebras. Department of Mathematics and Statistics, Carleton University and Fakultät für Mathematik, Universität Bielefeld, 1-10.
[7]
Hernández, J.F. (2004) Sobre as algebras estandarmente estratificadas. PhD Thesis Presented on Mathematics and Statistics Institute of Sao Paulo University, Brasil. (In Portuguese)
[8]
Platzeck, M.I. and Reiten, I. (2001) Modules of Finite Projective Dimension for Standardly Stratified Algebras. Communications in Algebra, 29, 973-986. http://dx.doi.org/10.1081/AGB-100001660
[9]
Sisodia, G. (2007) Nakayama Algebras. University of Sao Paulo, Brasil, 1-8.
[10]
Tan, R. (2013) Auslander Algebras of Self-Injective Nakayama Algebras. Department of Mathematics, Hubei University, China, 89-99.
[11]
Ochoa, R.F. (2014) Stratification Analysis of Certain Nakayama Algebras. Master’s Thesis Presented on Faculty of Mathematics and Computer Sciences of Havana University, Cuba.
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) are not standardly stratified or costandardly stratified.
