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On Mutual Definability of Operations on Fields. / Korotkova, R. M.; Kudinov, O. V.; Morozov, A. S.

In: Siberian Mathematical Journal, Vol. 60, No. 6, 01.11.2019, p. 1032-1039.

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

Harvard

Korotkova, RM, Kudinov, OV & Morozov, AS 2019, 'On Mutual Definability of Operations on Fields', Siberian Mathematical Journal, vol. 60, no. 6, pp. 1032-1039. https://doi.org/10.1134/S0037446619060119

APA

Korotkova, R. M., Kudinov, O. V., & Morozov, A. S. (2019). On Mutual Definability of Operations on Fields. Siberian Mathematical Journal, 60(6), 1032-1039. https://doi.org/10.1134/S0037446619060119

Vancouver

Korotkova RM, Kudinov OV, Morozov AS. On Mutual Definability of Operations on Fields. Siberian Mathematical Journal. 2019 Nov 1;60(6):1032-1039. doi: 10.1134/S0037446619060119

Author

Korotkova, R. M. ; Kudinov, O. V. ; Morozov, A. S. / On Mutual Definability of Operations on Fields. In: Siberian Mathematical Journal. 2019 ; Vol. 60, No. 6. pp. 1032-1039.

BibTeX

@article{7df9ead3a91446fda4fba63b889b78bc,
title = "On Mutual Definability of Operations on Fields",
abstract = "We study the possibilities of defining some operations on fields via the remaining operations. In particular, we prove that multiplication on an arbitrary field can be defined via addition if and only if the field is a finite extension of its prime subfield. We give a sufficient condition for the nondefinability of addition via multiplication and demonstrate that multiplication and addition on the reals and complexes cannot be mutually defined by means of the relations with parameters which are preserved under automorphisms. We also describe the mutual definability of addition, multiplication, and exponentiation via the remaining two operations.",
keywords = "definability, exponentiation, field",
author = "Korotkova, {R. M.} and Kudinov, {O. V.} and Morozov, {A. S.}",
year = "2019",
month = nov,
day = "1",
doi = "10.1134/S0037446619060119",
language = "English",
volume = "60",
pages = "1032--1039",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",
number = "6",

}

RIS

TY - JOUR

T1 - On Mutual Definability of Operations on Fields

AU - Korotkova, R. M.

AU - Kudinov, O. V.

AU - Morozov, A. S.

PY - 2019/11/1

Y1 - 2019/11/1

N2 - We study the possibilities of defining some operations on fields via the remaining operations. In particular, we prove that multiplication on an arbitrary field can be defined via addition if and only if the field is a finite extension of its prime subfield. We give a sufficient condition for the nondefinability of addition via multiplication and demonstrate that multiplication and addition on the reals and complexes cannot be mutually defined by means of the relations with parameters which are preserved under automorphisms. We also describe the mutual definability of addition, multiplication, and exponentiation via the remaining two operations.

AB - We study the possibilities of defining some operations on fields via the remaining operations. In particular, we prove that multiplication on an arbitrary field can be defined via addition if and only if the field is a finite extension of its prime subfield. We give a sufficient condition for the nondefinability of addition via multiplication and demonstrate that multiplication and addition on the reals and complexes cannot be mutually defined by means of the relations with parameters which are preserved under automorphisms. We also describe the mutual definability of addition, multiplication, and exponentiation via the remaining two operations.

KW - definability

KW - exponentiation

KW - field

UR - http://www.scopus.com/inward/record.url?scp=85079732041&partnerID=8YFLogxK

U2 - 10.1134/S0037446619060119

DO - 10.1134/S0037446619060119

M3 - Article

AN - SCOPUS:85079732041

VL - 60

SP - 1032

EP - 1039

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 6

ER -

ID: 23593447