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

Dobbs, David E.; Picavet, Gabriel

doi:10.5802/ambp.175

Dobbs, David E.¹ ; Picavet, Gabriel 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, Tome 10 (2003) no. 2, pp. 245-260.

Résumé

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 $A [X_{1}, \dots, X_{n}] ↪ B [X_{1}, \dots, X_{n}]$ satisfies GB for each $n \geq 0$ . However, for any nonzero ring $A$ and indeterminate $X$ over $A$ , the inclusion map $A ↪ A [X]$ is not universally (S)GB.

MR Zbl

DOI : 10.5802/ambp.175

Affiliations des auteurs :

Dobbs, David E. ¹ ; Picavet, Gabriel 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

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     author = {Dobbs, David E. and Picavet, Gabriel},
     title = {On {Strong} {Going-Between,} {Going-Down,} {And} {Their} {Universalizations,} {II}},
     journal = {Annales math\'ematiques Blaise Pascal},
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     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {10},
     number = {2},
     year = {2003},
     doi = {10.5802/ambp.175},
     zbl = {1071.13003},
     mrnumber = {2031270},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/ambp.175/}
}

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Dobbs, David E.; Picavet, Gabriel. On Strong Going-Between, Going-Down, And Their Universalizations, II. Annales mathématiques Blaise Pascal, Tome 10 (2003) no. 2, pp. 245-260. doi : 10.5802/ambp.175. http://www.numdam.org/articles/10.5802/ambp.175/

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