On the Schröder-Bernstein property for abelian groups

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10509758" target="_blank" >RIV/00216208:11320/25:10509758 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=2xj6aiKsJ9" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=2xj6aiKsJ9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/00927872.2024.2430401" target="_blank" >10.1080/00927872.2024.2430401</a>

Result language
angličtina
Original language name
On the Schröder-Bernstein property for abelian groups
Original language description
A right R-module M satisfies the Schröder-Bernstein property, if whenever direct summands, say N and K, of M are d-subisomorphic to each other (i.e. if N is isomorphic to a direct summand of K and K is isomorphic to a directsummand of N), then N TILDE OPERATOR+D91= K. The module M is said to be ADS (Absolute Direct Summand) if for every decomposition M = SCIRCLED PLUS T and every complement A of S, we have M = SCIRCLED PLUS A. We primarily show that the question, whether ADS abelian groups satisfying the Schröder-Bernstein property, has a positive answer. Thenwe consider a related problem on the property C2 (a group G is C2 if whenever A is a summand of G and B is a subgroup of G isomorphic to A, then B is also a summand of G) and we present several sufficient conditions of C2 abelian groups to satisfy the Schröder-Bernstein property.
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

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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