On Strong Going-Between, Going-Down, And Their Universalizations, II

David E. Dobbs[1]; Gabriel Picavet[2]

  • [1] University of Tennessee Department of Mathematics Knoxville, Tennessee 37996-1300 U.S.A.
  • [2] Université Blaise Pascal Laboratoire de Mathématiques Pures 63177 Aubière Cedex FRANCE

Annales mathématiques Blaise Pascal (2003)

  • Volume: 10, Issue: 2, page 245-260
  • ISSN: 1259-1734

Abstract

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We consider analogies between the logically independent properties of strong going-between (SGB) and going-down (GD), as well as analogies between the universalizations of these properties. Transfer results are obtained for the (universally) SGB property relative to pullbacks and Nagata ring constructions. It is shown that if A ⊆ B are domains such that A is an LFD universally going-down domain and B is algebraic over A , then the inclusion map A [ X 1 , ⋯ , X n ] ↪ B [ X 1 , ⋯ , X n ] satisfies GB for each n ≥ 0 . However, for any nonzero ring A and indeterminate X over A , the inclusion map A ↪ A [ X ] is not universally (S)GB.

How to cite

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Dobbs, David E., and Picavet, Gabriel. "On Strong Going-Between, Going-Down, And Their Universalizations, II." Annales mathématiques Blaise Pascal 10.2 (2003): 245-260. <http://eudml.org/doc/10488>.

@article{Dobbs2003,
abstract = {We consider analogies between the logically independent properties of strong going-between (SGB) and going-down (GD), as well as analogies between the universalizations of these properties. Transfer results are obtained for the (universally) SGB property relative to pullbacks and Nagata ring constructions. It is shown that if $A \subseteq B$ are domains such that $A$ is an LFD universally going-down domain and $B$ is algebraic over $A$, then the inclusion map $A[X_1, \, \dots , \, X_n] \hookrightarrow B[X_1, \, \dots , \, X_n]$ satisfies GB for each $n \ge 0$. However, for any nonzero ring $A$ and indeterminate $X$ over $A$, the inclusion map $A \hookrightarrow A[X]$ is not universally (S)GB.},
affiliation = {University of Tennessee Department of Mathematics Knoxville, Tennessee 37996-1300 U.S.A.; Université Blaise Pascal Laboratoire de Mathématiques Pures 63177 Aubière Cedex FRANCE},
author = {Dobbs, David E., Picavet, Gabriel},
journal = {Annales mathématiques Blaise Pascal},
keywords = {strongly going-between domain; going-down domain; universalization; pullback; Nagata ring},
language = {eng},
month = {7},
number = {2},
pages = {245-260},
publisher = {Annales mathématiques Blaise Pascal},
title = {On Strong Going-Between, Going-Down, And Their Universalizations, II},
url = {http://eudml.org/doc/10488},
volume = {10},
year = {2003},
}

TY - JOUR
AU - Dobbs, David E.
AU - Picavet, Gabriel
TI - On Strong Going-Between, Going-Down, And Their Universalizations, II
JO - Annales mathématiques Blaise Pascal
DA - 2003/7//
PB - Annales mathématiques Blaise Pascal
VL - 10
IS - 2
SP - 245
EP - 260
AB - We consider analogies between the logically independent properties of strong going-between (SGB) and going-down (GD), as well as analogies between the universalizations of these properties. Transfer results are obtained for the (universally) SGB property relative to pullbacks and Nagata ring constructions. It is shown that if $A \subseteq B$ are domains such that $A$ is an LFD universally going-down domain and $B$ is algebraic over $A$, then the inclusion map $A[X_1, \, \dots , \, X_n] \hookrightarrow B[X_1, \, \dots , \, X_n]$ satisfies GB for each $n \ge 0$. However, for any nonzero ring $A$ and indeterminate $X$ over $A$, the inclusion map $A \hookrightarrow A[X]$ is not universally (S)GB.
LA - eng
KW - strongly going-between domain; going-down domain; universalization; pullback; Nagata ring
UR - http://eudml.org/doc/10488
ER -

References

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