Generalized Injectivity and Approximations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10331691" target="_blank" >RIV/00216208:11320/16:10331691 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1080/00927872.2015.1087548" target="_blank" >http://dx.doi.org/10.1080/00927872.2015.1087548</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/00927872.2015.1087548" target="_blank" >10.1080/00927872.2015.1087548</a>

Result language
angličtina
Original language name
Generalized Injectivity and Approximations
Original language description
Injective, pure-injective, and fp-injective modules are well known to provide for approximations in the category Mod-R for an arbitrary ring R. We prove that this fails for many other generalizations of injectivity: the C-1, C-2, C-3, quasi-continuous, continuous, and quasi-injective modules. We show that, except for the class of all C-1-modules, each of the latter classes provides for approximations only when it coincides with the injectives (for quasi-injective modules, this forces R to be a right noetherian V-ring; in the other cases, R even has to be semisimple artinian). The class of all C-1-modules over a right noetherian ring R is (pre)enveloping iff R is a certain right artinian ring of Loewy length 2; in this case, however, R may have an arbitrary representation type.
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

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

Similar results(10)