Very flat, locally very flat, and contraadjusted modules

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10331695" target="_blank" >RIV/00216208:11320/16:10331695 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jpaa.2016.05.020" target="_blank" >http://dx.doi.org/10.1016/j.jpaa.2016.05.020</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpaa.2016.05.020" target="_blank" >10.1016/j.jpaa.2016.05.020</a>

Result language
angličtina
Original language name
Very flat, locally very flat, and contraadjusted modules
Original language description
Very flat and contraadjusted modules naturally arise in algebraic geometry in the study of contraherent cosheaves over schemes. Here, we investigate the structure and approximation properties of these modules over commutative noetherian rings. Using an analogy between projective and flat Mittag-Leffler modules on one hand, and very fiat and locally very flat modules on the other, we prove that each of the following statements are equivalent to the finiteness of the Zariski spectrum Spec(R) of a noetherian domain R: (i) the class of all very flat modules is covering, (ii) the class of all locally very flat modules is precovering, and (ill) the class of all contraadjusted modules is enveloping. We also prove an analog of Pontryagin's Criterion for locally very flat modules over Dedekind domains.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA14-15479S" target="_blank" >GA14-15479S: Representation Theory (Structural Decompositions and Their Constraints)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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