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001 on1381680652;

003 OCoLC;

005 20260527041718.0;

006 m o d ;

007 cr unu||||||||;

008 230609s2023 ncu obm 000 0 eng d;

035 a| (OCoLC)1381680652;

090 a| QA247;

049 a| EREE;

100 1 a| Kardos, Michael,e| author.=| ^A1191535;

245 10 a| First order definition of rings using group of units /c| by Michael Kardos.;

264 1 a| [Greenville, N.C.] :b| [East Carolina University],c| 2023.;

300 a| 1 online resource (42 pages);

336 a| textb| txt2| rdacontent;

337 a| computerb| c2| rdamedia;

338 a| online resourceb| cr2| rdacarrier;

347 a| text fileb| PDFc| 305.8 KB2| rda;

538 a| System requirements: Adobe Reader.;

538 a| Mode of access: World Wide Web.;

502 b| M.A.c| East Carolina Universityd| 2023.;

500 a| Presented to the Faculty of the Department of Mathematics;

500 a| Advisor: Alexandra Shlapentokh;

500 a| Title from PDF t.p. (viewed September 5, 2024).;

520 3 a| We discuss the technical background and relevant research regarding the undecidability of OQab. Given an algebraic extension K/Q, we consider the subring defined by RK={x [epsilon] OK \[for-all] [epsilon] UK \ {1\}\ [exists][delta]\in UK\[delta]-1\[equivalent] x([epsilon]-1) mod ([epsilon]-1)^²}.We later consider a similar construction over subrings of Q of characteristic 0. In doing this, we hope to gain insight into the result of the construction of RK when K=Qab.;

504 a| Includes bibliographical references.;

650 0 a| Number theory.=| ^A22877;

650 0 a| Definability theory (Mathematical logic)=| ^A78222;

650 0 a| Equations, Abelian.=| ^A279435;

653 a| subring;

653 a| extension;

653 a| unit;

700 1 a| Shlapentokh, Alexandra,e| degree supervisor.1| https://id.oclc.org/worldcat/entity/E39PCjHvHxRfjR8Bqr766rfF83=| ^A704412;

710 2 a| East Carolina University.b| Department of Mathematics.?| UNAUTHORIZED;

856 40 z| Access via ScholarShipu| http://hdl.handle.net/10342/12855;

994 a| C0b| ERE;

596 a| 1 4;

998 a| 6143753;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6143753-1001l| JNETm| JOYNERr| Ys| Yt| JNE3ETDu| 6/9/2023x| ETDz| JERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6143753-2001l| HSLELECm| HSLr| Ys| Yt| HEETDu| 6/9/2023x| ETDz| HERESOURCE;

First order definition of rings using group of units / by Michael Kardos.

Author/creator	Kardos, Michael author.
Other author	Shlapentokh, Alexandra, degree supervisor.
Other author	East Carolina University. Department of Mathematics.
Format	Theses and dissertations
Publication	[Greenville, N.C.] : [East Carolina University], 2023.
Description	1 online resource (42 pages)
Supplemental Content	Access via ScholarShip
Subjects	Number theory. Definability theory (Mathematical logic) Equations, Abelian.

Summary	We discuss the technical background and relevant research regarding the undecidability of OQab. Given an algebraic extension K/Q, we consider the subring defined by RK={x [epsilon] OK \[for-all] [epsilon] UK \ {1\}\ [exists][delta]\in UK\[delta]-1\[equivalent] x([epsilon]-1) mod ([epsilon]-1)^²}.We later consider a similar construction over subrings of Q of characteristic 0. In doing this, we hope to gain insight into the result of the construction of RK when K=Qab.
General note	Presented to the Faculty of the Department of Mathematics
General note	Advisor: Alexandra Shlapentokh
General note	Title from PDF t.p. (viewed September 5, 2024).
Dissertation note	M.A. East Carolina University 2023.
Bibliography note	Includes bibliographical references.
Technical details	System requirements: Adobe Reader.
Technical details	Mode of access: World Wide Web.

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First order definition of rings using group of units / by Michael Kardos.

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