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Weak diamond, weak projectivity, and transfinite extensions of simple artinian rings *
We apply set-theoretic methods to study projective modules and their generalizations over transfinite extensions of simple artinian rings R. We prove that if R is small, then the Weak Diamond implies that proje...
Pure mathematics
- 2022 •
- Jimp •
- Link
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
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Test sets for factorization properties of modules
bar R vertical bar, then the category of all projective modules is kappaBaer's Criterion of injectivity implies that injectivity of a module in dependence on the algebraic structure of the underlying ring
Pure mathematics
- 2020 •
- Jimp •
- Link
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
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FAITH'S PROBLEM ON R-PROJECTIVITY IS UNDECIDABLE
asked for what rings R does the Dual Baer Criterion hold in Mod-R, that is, when does R-projectivity imply projectivity for all right R-modules? Such rings R were such that the ...
Pure mathematics
- 2019 •
- Jimp •
- Link
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
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INFINITELY GENERATED PROJECTIVE MODULES OVER PULLBACKS OF RINGS
generated projective left R-modules is determined by the monoid D(M) defined inequalities as the monoid of isomorphism classes of countably generated projective right R rings such that all its project...
BA - Obecná matematika
- 2014 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Flat ring epimorphisms of countable type
-module. Assume that the related Gabriel topology of right ideals in R has a countable base. Then we show that the left R-module U has projective dimension at most 1 in the category of left R-...
Pure mathematics
- 2020 •
- Jimp •
- Link
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
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Pure Projective Tilting Modules
Let TR be a 1-tilting module with tilting torsion pair (Gen T,F) in Mod-R. The following conditions are proved to be equivalent: (1) T is pure projective; (2) Gen T is a definable subcategory of Mod-R with enough p...
Pure mathematics
- 2020 •
- JSC •
- Link
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JSC - Článek v periodiku v databázi SCOPUS
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Classes of Flat Modules Arising in Algebraic Geometry and Approximations
Abstract Locally projective (i.e., flat Mittag-Leffler) modules are known to provide for approximations only over perfect rings. Recently, very flat modules were=Spec(R) X=Spec(R) , where R is a N...
BA - Obecná matematika
- 2016 •
- D •
- Link
Rok uplatnění
D - Stať ve sborníku
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Classifying Modules in Add of a Class of Modules with Semilocal Endomorphism Rings
We present a dimension theory for modules in Add(C), where C is a class of modules with semilocal endomorphism rings satisfying certain smallness conditions. For example, if C is the class of all finitely presented modules ...
Pure mathematics
- 2020 •
- D •
- Link
Rok uplatnění
D - Stať ve sborníku
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A version of the Baer splitting problem for noetherian rings
We call a module M over a commutative noetherian ring R quasi-Baer in case Ext (M,T) = 0 for each locally artinian (= semiartinian) module T. We prove that all quasi--Baer modules are projective provided t...
BA - Obecná matematika
- 2008 •
- C
Rok uplatnění
C - Kapitola v odborné knize
Flat commutative ring epimorphisms of almost Krull dimension zero
dimension zero. Under these assumptions, we show that the projective dimension of the R subcategory to the R-module U in R-Mod. Assuming additionally that the ring U and all the rings R/I are per...
Pure mathematics
- 2023 •
- Jimp •
- Link
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
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