ON SEMIGENERIC TAMENESS AND BASE FIELD EXTENSION
Glasgow mathematical journal, Tome 58 (2016) no. 1, pp. 39-53

Voir la notice de l'article provenant de la source Cambridge University Press

The notions of central endolength and semigeneric tameness are introduced, and their behaviour under base field extension for finite-dimensional algebras over perfect fields are analysed. For k a perfect field, K an algebraic closure and Λ a finite-dimensional k-algebra, here there is a proof that Λ is semigenerically tame if and only if Λ ⊗kK is tame.
PÉREZ, EFRÉN. ON SEMIGENERIC TAMENESS AND BASE FIELD EXTENSION. Glasgow mathematical journal, Tome 58 (2016) no. 1, pp. 39-53. doi: 10.1017/S0017089515000051
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[1] 1.Anderson, F. and Fuller, K., Rings and categories of modules, Graduate texts in Math. 13, (Springer-Verlag, Berlin-Heidelberg-New York, 1973). Google Scholar

[2] 2.Auslander, M., Reiten, I. and Smalø, S., Representation theory of Artin algebras, Cambridge Studies in Advanced Mathematics, vol. 36 (Cambridge University Press, Cambridge, 1995). Google Scholar | DOI

[3] 3.Bautista, R., Pérez, E. and Salmerón, L., On restrictions of indecomposables of tame algebras, Colloq. Math. 124 (2011), 35–60. Google Scholar | DOI

[4] 4.Bautista, R., Pérez, E. and Salmerón, L., On generically tame algebras over perfect fields, Adv. Math. 231 (2012), 436–481. Google Scholar | DOI

[5] 5.Bautista, R., Salmerón, L. and Zuazua, R., Differential tensor algebras and their module categories, London Mathematical Society Lecture Notes Series, vol. 362 (Cambridge University Press, Cambridge-New York, 2009). Google Scholar | DOI

[6] 6.Crawley-Boevey, W. W., Tame algebras and generic modules, Proc. London Math. Soc. 63 (3) (1991), 241–265. Google Scholar | DOI

[7] 7.Crawley-Boevey, W. W., Modules of finite length over their endomorphism rings, in Representations of algebras and related topics, (Brenner, S. and Tachikawa, H., Editors) London Math. Lect. Notes Series, vol. 168 (1992), 127–184. Google Scholar

[8] 8.De-Vicente, J., Guerrero, E. and Pérez, E., On the endomorphism rings of generic modules of tame triangular matrix algebras over real closed fields, Aportaciones Matemáticas 45 (2012), 17–53. Google Scholar

[9] 9.Dlab, V. and Ringel, C. M., Real subspaces of a quaternion vector space, Can. J. Math. XXX No.6 (1978), 1228–1242. Google Scholar | DOI

[10] 10.Drozd, Yu. A., Tame and wild matrix problems, in Representations and quadratic forms [Institute of Mathematics, Academic of Sciences, Ukranian SSR, Kiev (1979) 39-47]; Amer. Math. Soc. Transl. 128 (1986), 31–55. Google Scholar

[11] 11.Jacobson, N., Lectures in abstract algebra, Vol. III, Theory of fields and Galois theory (Springer-Verlag, Princeton, 1964). Google Scholar

[12] 12.Kasjan, S., Auslander-Reiten sequences and base field extensions, Proc. Amer. Math. Soc. 128 (10) (2000), 2885–2896. Google Scholar | DOI

[13] 13.Kasjan, S., Base field extensions and generic modules over finite dimensional algebras, Arch. Math. 77 (2001), 155–162. Google Scholar | DOI

[14] 14.Méndez, G. and Pérez, E., A remark on generic tameness preservation under base field extension, J. Algebra Appl. 12 (4) (2013), 1250183-1–1250183-4. Google Scholar | DOI

[15] 15.Rowen, L. H., Ring theory (Student Edition) (Academic Press, San Diego-London, 1991). Google Scholar

[16] 16.Silver, L., Noncommutative localizations and applications, J. Algebra 7 (1967), 44–76. Google Scholar | DOI

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