Tame three-partite subamalgams of tiled orders of polynomial growth

Daniel Simson

Colloquium Mathematicae (1999)

  • Volume: 81, Issue: 2, page 237-262
  • ISSN: 0010-1354

Abstract

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Assume that K is an algebraically closed field. Let D be a complete discrete valuation domain with a unique maximal ideal p and residue field D/p ≌ K. We also assume that D is an algebra over the field K . We study subamalgam D-suborders Λ • (1.2) of tiled D-orders Λ (1.1). A simple criterion for a tame lattice type subamalgam D-order Λ • to be of polynomial growth is given in Theorem 1.5. Tame lattice type subamalgam D-orders Λ • of non-polynomial growth are completely described in Theorem 6.2 and Corollary 6.3.

How to cite

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Simson, Daniel. "Tame three-partite subamalgams of tiled orders of polynomial growth." Colloquium Mathematicae 81.2 (1999): 237-262. <http://eudml.org/doc/210737>.

@article{Simson1999,
abstract = {Assume that K is an algebraically closed field. Let D be a complete discrete valuation domain with a unique maximal ideal p and residue field D/p ≌ K. We also assume that D is an algebra over the field K . We study subamalgam D-suborders $Λ^•$ (1.2) of tiled D-orders Λ (1.1). A simple criterion for a tame lattice type subamalgam D-order $Λ^•$ to be of polynomial growth is given in Theorem 1.5. Tame lattice type subamalgam D-orders $Λ^•$ of non-polynomial growth are completely described in Theorem 6.2 and Corollary 6.3.},
author = {Simson, Daniel},
journal = {Colloquium Mathematicae},
keywords = {forbidden substructures; tame orders of polynomial growth; tame three-partite subamalgams; matrix algebras; amalgamations; integral quadratic forms; hypercritical two-peak posets; two-peak garlands},
language = {eng},
number = {2},
pages = {237-262},
title = {Tame three-partite subamalgams of tiled orders of polynomial growth},
url = {http://eudml.org/doc/210737},
volume = {81},
year = {1999},
}

TY - JOUR
AU - Simson, Daniel
TI - Tame three-partite subamalgams of tiled orders of polynomial growth
JO - Colloquium Mathematicae
PY - 1999
VL - 81
IS - 2
SP - 237
EP - 262
AB - Assume that K is an algebraically closed field. Let D be a complete discrete valuation domain with a unique maximal ideal p and residue field D/p ≌ K. We also assume that D is an algebra over the field K . We study subamalgam D-suborders $Λ^•$ (1.2) of tiled D-orders Λ (1.1). A simple criterion for a tame lattice type subamalgam D-order $Λ^•$ to be of polynomial growth is given in Theorem 1.5. Tame lattice type subamalgam D-orders $Λ^•$ of non-polynomial growth are completely described in Theorem 6.2 and Corollary 6.3.
LA - eng
KW - forbidden substructures; tame orders of polynomial growth; tame three-partite subamalgams; matrix algebras; amalgamations; integral quadratic forms; hypercritical two-peak posets; two-peak garlands
UR - http://eudml.org/doc/210737
ER -

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