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On Lifting Modules and Weak Lifting Modules
Tutuncu, Derya Keskin,Tribak, Rachid Department of Mathematics 2005 Kyungpook mathematical journal Vol.45 No.3
We say that a module M is weak lifting if M is supplemented and every supplement submodule of M is a direct summand. The module M is called lifting, if it is weak lifting and amply supplemented. This paper investigates the structure of weak lifting modules and lifting modules having small radical over commutative noetherian rings.
Some Results on Simple-Direct-Injective Modules
Derya Keskin Tutuncu,Rachid Tribak 경북대학교 자연과학대학 수학과 2023 Kyungpook mathematical journal Vol.63 No.4
A module M is called a simple-direct-injective module if, whenever A and B are simple submodules of M with A∼=B and B is a direct summand of M, then A is a direct summand of M. Some new characterizations of these modules are proved. The structure of simple-direct-injective modules over a commutative Dedekind domain is fully determined. Also, some relevant counterexamples are indicated to show that a left simple direct-injective ring need not be right simple-direct-injective.
Baer-Kaplansky Theorem for Modules over Non-commutative Algebras
D'Este, Gabriella,Tutuncu, Derya KeskIn Department of Mathematics 2021 Kyungpook mathematical journal Vol.61 No.2
In this paper we investigate the Baer-Kaplansky theorem for module classes on algebras of finite representation types over a field. To do this we construct finite dimensional quiver algebras over any field.
Two-step polarization reversal in biased ferroelectrics
Daniels, John E.,Cozzan, Clayton,Ukritnukun, Supphatuch,Tutuncu, Goknur,Andrieux, Jerome,Glaum, Julia,Dosch, Chris,Jo, Wook,Jones, Jacob L. American Institute of Physics 2014 JOURNAL OF APPLIED PHYSICS - Vol.115 No.22
Polarization reversal in polycrystalline ferroelectrics is shown to occur via two distinct and sequential domain reorientation steps. This reorientation sequence, which cannot be readily discriminated in the overall sample polarization, is made apparent using time-resolved high-energy x-ray diffraction. Upon application of electric fields opposite to the initial poling direction, two unique and significantly different time constants are observed. The first (faster time constant) is shown to be derived by the release of a residual stress due to initial electrical biasing and the second (slower time constant) due to the redevelopment of residual stress during further domain wall motion. A modified domain reorientation model is given that accurately describes the domain volume fraction evolution during the reversal process. (C) 2014 AIP Publishing LLC.