Representation-finite triangular algebras form an open scheme

Stanisław Kasjan

Open Mathematics (2003)

  • Volume: 1, Issue: 1, page 97-107
  • ISSN: 2391-5455

Abstract

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Let V be a valuation ring in an algebraically closed field K with the residue field R. Assume that A is a V-order such that the R-algebra Ā obtained from A by reduction modulo the radical of V is triangular and representation-finite. Then the K-algebra KA ≅ A ⊗V is again triangular and representation-finite. It follows by the van den Dries’s test that triangular representation-finite algebras form an open scheme.

How to cite

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Stanisław Kasjan. "Representation-finite triangular algebras form an open scheme." Open Mathematics 1.1 (2003): 97-107. <http://eudml.org/doc/268752>.

@article{StanisławKasjan2003,
abstract = {Let V be a valuation ring in an algebraically closed field K with the residue field R. Assume that A is a V-order such that the R-algebra Ā obtained from A by reduction modulo the radical of V is triangular and representation-finite. Then the K-algebra KA ≅ A ⊗V is again triangular and representation-finite. It follows by the van den Dries’s test that triangular representation-finite algebras form an open scheme.},
author = {Stanisław Kasjan},
journal = {Open Mathematics},
keywords = {16G60; 16G30; 03C60},
language = {eng},
number = {1},
pages = {97-107},
title = {Representation-finite triangular algebras form an open scheme},
url = {http://eudml.org/doc/268752},
volume = {1},
year = {2003},
}

TY - JOUR
AU - Stanisław Kasjan
TI - Representation-finite triangular algebras form an open scheme
JO - Open Mathematics
PY - 2003
VL - 1
IS - 1
SP - 97
EP - 107
AB - Let V be a valuation ring in an algebraically closed field K with the residue field R. Assume that A is a V-order such that the R-algebra Ā obtained from A by reduction modulo the radical of V is triangular and representation-finite. Then the K-algebra KA ≅ A ⊗V is again triangular and representation-finite. It follows by the van den Dries’s test that triangular representation-finite algebras form an open scheme.
LA - eng
KW - 16G60; 16G30; 03C60
UR - http://eudml.org/doc/268752
ER -

References

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