Abstract
A polynomial p(x_1,…,x_n ) in the polynomial algebra K[X_n ]=K[x_1,…,x_n ] in n commuting variables is called symmetric if p(x_1,…,x_n )=p(x_σ(1) ,…,x_σ(n) ) for each permutation σ in the symmetric group S_n. The set 〖K[X_n ]〗^(S_n ) of symmetric polynomials is the algebra of S_n-invariants. The algebra 〖K[X_n ]〗^(S_n ) is generated by n algebraically independent elements called elementary symmetric polynomials. The idea in the commutative algebra K[X_n ] was generalized for noncommutative relatively free algebras F_n of rank n; and generating sets for the algebra F_n^(S_n ) were investigated. In this study, we review recent works on symmetric polynomials in the free metabelian associative algebras and the free metabelian Lie algebras.
Ethical Statement
In the study, the authors declare that there is no violation of research and publication ethics and that the study does not require ethics committee approval.
Supporting Institution
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References
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Details
| Primary Language | English |
|---|---|
| Subjects | Algebra and Number Theory |
| Journal Section | Review |
| Authors | |
| Submission Date | September 3, 2025 |
| Acceptance Date | September 19, 2025 |
| Early Pub Date | December 26, 2025 |
| Publication Date | December 29, 2025 |
| Published in Issue | Year 2025 Volume: 1 Issue: 1 |
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Aktif araştırma alanları; Coğrafi Bilgi Sistemi (CBS) ve Uzaktan Algılama (UA) tekniklerini kullanarak; yeraltı sularının kirlenmeye karşı hassasiyetinin ve potansiyelinin değerlendirilmesi, yer seçimi, çeşitli coğrafi unsurlara ait morfometrik özelliklerinin belirlenmesi, arazi kullanımına ait zamansal değişimlerin, yüzey sıcaklığının ve bitki örtüsünün haritalanması ve belirlenmesi konularını içermektedir.
Caner Ozdemir received the B.S.E.E. degree in 1992 from the Middle East Technical University, Ankara, Turkey, and the M.S.E. and Ph. D. degrees in Electrical & Computer Engineering from the University of Texas at Austin in 1995 and 1998, respectively.
From 1992 to 1993, he worked as a project engineer at the Electronic Warfare Programs Directorate of ASELSAN Electronic Industries Inc., Ankara, Turkey. From 1998 to 2000, he worked as a research scientist at Electronic & Avionics Systems (ASTG) group of AlliedSignal Inc., Columbia, Maryland. He joined the faculty of Mersin University in 2000 and is currently a professor in the department of Electrical-Electronics Engineering, Mersin, Turkey. He has been serving as a consultant to the Marmara Research Center of the Scientific and Research Council (TUBITAK) of Turkey and many defense industry firms. Dr. Ozdemir’s research interests are radar cross section, radar image/signal processing, inverse synthetic aperture radar (ISAR), radar cross section, ground penetrating radar, through-the-wall imaging radar and antenna design. He has published more than 180 journal articles and conference/symposium papers on these subjects.
Dr. Ozdemir is a recipient of URSI EMT-S Young Scientist Award in the 2004 International Symposium on Electromagnetic Theory in Pisa, Italy and also recipient of a JARS best paper award for photo-optical instrumentation published in the Journal of Applied Remote Sensing in 2016. He is the author of the book titled “Inverse Synthetic Aperture Radar Imaging with Matlab Algorithms”.
nanometarial, silica aerogel, carbon nanotube, graphene, high entropy alloy
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