On Hypergraphs of Minimal and Prime Models of Theories of Abelian Groups

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On Hypergraphs of Minimal and Prime Models of Theories of Abelian Groups. / Sudoplatov, S. V.

In: Siberian Electronic Mathematical Reports, Vol. 17, 2020, p. 1137-1154.

Research output: Contribution to journal › Article › peer-review

Harvard

Sudoplatov, SV 2020, 'On Hypergraphs of Minimal and Prime Models of Theories of Abelian Groups', Siberian Electronic Mathematical Reports, vol. 17, pp. 1137-1154. https://doi.org/10.33048/semi.2020.17.086

APA

Sudoplatov, S. V. (2020). On Hypergraphs of Minimal and Prime Models of Theories of Abelian Groups. Siberian Electronic Mathematical Reports, 17, 1137-1154. https://doi.org/10.33048/semi.2020.17.086

Vancouver

Sudoplatov SV. On Hypergraphs of Minimal and Prime Models of Theories of Abelian Groups. Siberian Electronic Mathematical Reports. 2020;17:1137-1154. doi: 10.33048/semi.2020.17.086

Author

Sudoplatov, S. V. / On Hypergraphs of Minimal and Prime Models of Theories of Abelian Groups. In: Siberian Electronic Mathematical Reports. 2020 ; Vol. 17. pp. 1137-1154.

BibTeX

@article{c053d9613130437c9172f919595ca6f8,

title = "On Hypergraphs of Minimal and Prime Models of Theories of Abelian Groups",

abstract = "We systematize known results about minimal and prime models of theories of abelian groups. Based on these results we describe properties and provide structural ones on hypergraphs of models for theories of abelian groups. In particular, we characterize non-emptiness and infiniteness of hypergraphs of minimal and prime models. We give necessary and sufficient conditions for almost disjointness of the respective hypergraphs. We also characterize conditions of preservation for non-emptiness and disjointness of hypergraphs of minimal and prime models at transformations to direct sums of groups.",

keywords = "abelian group, elementary theory, hypergraph of models, minimal model, prime model",

author = "Sudoplatov, {S. V.}",

year = "2020",

doi = "10.33048/semi.2020.17.086",

language = "English",

volume = "17",

pages = "1137--1154",

journal = "Сибирские электронные математические известия",

issn = "1813-3304",

publisher = "Sobolev Institute of Mathematics",

}

RIS

TY - JOUR

T1 - On Hypergraphs of Minimal and Prime Models of Theories of Abelian Groups

AU - Sudoplatov, S. V.

PY - 2020

Y1 - 2020

N2 - We systematize known results about minimal and prime models of theories of abelian groups. Based on these results we describe properties and provide structural ones on hypergraphs of models for theories of abelian groups. In particular, we characterize non-emptiness and infiniteness of hypergraphs of minimal and prime models. We give necessary and sufficient conditions for almost disjointness of the respective hypergraphs. We also characterize conditions of preservation for non-emptiness and disjointness of hypergraphs of minimal and prime models at transformations to direct sums of groups.

AB - We systematize known results about minimal and prime models of theories of abelian groups. Based on these results we describe properties and provide structural ones on hypergraphs of models for theories of abelian groups. In particular, we characterize non-emptiness and infiniteness of hypergraphs of minimal and prime models. We give necessary and sufficient conditions for almost disjointness of the respective hypergraphs. We also characterize conditions of preservation for non-emptiness and disjointness of hypergraphs of minimal and prime models at transformations to direct sums of groups.

KW - abelian group

KW - elementary theory

KW - hypergraph of models

KW - minimal model

KW - prime model

UR - http://www.scopus.com/inward/record.url?scp=85099349053&partnerID=8YFLogxK

U2 - 10.33048/semi.2020.17.086

DO - 10.33048/semi.2020.17.086

M3 - Article

AN - SCOPUS:85099349053

VL - 17

SP - 1137

EP - 1154

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -

ID: 27504398