Generalizations of projectivity and supplements revisited for superfluous ideals

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10397911" target="_blank" >RIV/00216208:11320/19:10397911 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=H01_qPXdt2" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=H01_qPXdt2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/00927872.2018.1468897" target="_blank" >10.1080/00927872.2018.1468897</a>

Result language
angličtina
Original language name
Generalizations of projectivity and supplements revisited for superfluous ideals
Original language description
We (re)introduce four ideal-related generalizations of classic module-theoretic notions: the ideal-superfluity, projective ideal-covers, the ideal-projectivity, and ideal-supplements. For a superfluous ideal I, the main theorem asserts the equivalence between the conditions: "I-supplements are direct summands in finitely generated projective modules"; "finitely generated I-projective modules are projective"; "projective modules with finitely generated factors modulo I are finitely generated"; "finitely generated flat modules with projective factors modulo I are projective." Moreover, we provide a property of the ideal I which is sufficient for the equivalence to hold true. The property is expressed in terms of idempotent-lifting in matrix rings.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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