WHEN COTORSION MODULES ARE PURE INJECTIVE

被引：12

作者：

Herzog, Ivo ^{[1
]}

Rothmaler, Philipp ^{[2
]}

机构：

[1] Ohio State Univ, Lima, OH 45804 USA

[2] CUNY, Bronx, NY 10453 USA

来源：

JOURNAL OF MATHEMATICAL LOGIC | 2009年 / 9卷 / 01期

关键词：

Modules; cotorsion; pure injective; pure projective; Mittag-Leffler; pseudoflat; quasiflat; abelian groups; pseudofinite; pseudo-torsion; rings; coherent; von Neumann regular; pure semisimple; subcategories; definable; purely resolving; preenveloping; covariantly finite; Ziegler spectrum; dcc on pp formulas or finite matrix subgroups; MODEL-THEORY;

D O I：

10.1142/S0219061309000835

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize rings over which every cotorsion module is pure injective (Xu rings) in terms of certain descending chain conditions and the Ziegler spectrum, which renders the classes of von Neumann regular rings and of pure semisimple rings as two possible extremes. As preparation, descriptions of pure projective and Mittag-Leffler preenvelopes with respect to so-called definable subcategories and of pure generation for such are derived, which may be of interest on their own. Infinitary axiomatizations lead to coherence results previously known for the special case of flat modules. Along with pseudoflat modules we introduce quasiflat modules, which arise naturally in the model-theoretic and the category-theoretic contexts.

引用

页码：63 / 102

页数：40