Yazar "Alkan, Mustafa" seçeneğine göre listele

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    MODULES AND THE SECOND CLASSICAL ZARISKI TOPOLOGY
    (Univ Studi Catania, Dipt Matematica, 2018) Ceken, Secil; Alkan, Mustafa
    Let R be an associative ring with identity and Spec(s)(M) denote the set of all second submodules of a right R-module M. In this paper, we present a number of new results for the second classical Zariski topology on Spec(s)(M) for a right R-module M. We obtain a characterization of semisimple modules by using the second spectrum of a module. We prove that if R is a ring such that every right primitive factor of R is right artinian, then every non-zero submodule of a second right R-module M is second if and only if M is a fully prime module. We give some equivalent conditions for Spec(s)(M) to be a Hausdorff space or T-i-space when the right R-module M has certain algebraic properties. We obtain characterizations of commutative Quasi-Frobenius and artinian rings by using topological properties of the second classical Zariski topology. We give a full characterization of the irreducible components of Spec(s)(M) for a non-zero injective right module M over a ring R such that every prime factor of R is right or left Goldie.
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    On Strongly 2-Absorbing Second Submodules
    (Amer Inst Physics, 2018) Ceken, Secil; Alkan, Mustafa
    In this paper, we study on the concept of strongly 2-absorbing second submodule which is a dual notion of 2-absorbing submodule and a generalization of second submodule. We give some properties and characterizations of this submodule class and investigate the relationships with second and secondary submodules.
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    A sheaf on the second spectrum of a module
    (Taylor & Francıs Inc, 2018) Ceken, Secil; Alkan, Mustafa
    Let R be a commutative ring with identity and Spec(5)(M) denote the set all second submodules of an R-module M. In this paper, we construct and study a sheaf of modules, denoted by O(N, M), on Spec(5)(M) equipped with the dual Zariski topology of M, where N is an R-module. We give a characterization of the sections of the sheaf O(N, M) in terms of the ideal transform module. We present some interrelations between algebraic properties of N and the sections of O(N, M). We obtain some morphisms of sheaves induced by ring and module homomorphisms.
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    Survival of patients with well-developed collaterals undergoing CABG or medical treatment: An observational case-controlled study
    (Turkish Soc Cardiology, 2012) Tatli, Ersan; Aktoz, Meryem; Cakar, Mehmet Akif; Dogan, Emir; Alkan, Mustafa; Ozalp, Bilhan
    Objective: The effects of coronary artery bypass grafting (CABG) on mortality have not been evaluated in patients with well-developed coronary collaterals. We investigated functional capacity, presence of angina, the occurrence of acute myocardial infarction, survival and mortality in patients with well-developed coronary collaterals both undergoing and refusing CABG. Methods: The study was designed as a retrospective observational case-controlled study. Seventy-eight patients undergoing coronary angiography were included in this study. They had critical occlusion in the proximal left anterior descending artery (LAD) with Rentrop-3 collateral circulation towards LAD, and to proceed with CABG has been suggested. The patients were divided in two groups; first group proceeding with CABG (n=40) and the second, rejecting the surgery (medical treatment group; n=38). The rates of survival, the incidence of angina pectoris and acute myocardial infarction as well as the functional capacities were evaluated in all patients. Survival rates were evaluated using Kaplan-Meier survival analysis. Results: No statistically significant difference was observed between the two groups regarding the baseline characteristics of patients, the presence of angina pectoris, the severity of angina pectoris according to CCS, the occurrence of acute myocardial infarction or stroke, and the functional capacity according to NYHA (p>0.05). Death due to cardiovascular reasons was observed in eight patients of CABG group and in five patients of medical treatment group (p=0.710). The 5-year survival rate was observed to be 80% in CABG group while it was observed to be 84% in the medical treatment group (p=0.730). Conclusion: There was no significant difference regarding the survival rates in patients with well-developed coronary collaterals proceeding with CABG or medical treatment. (Anadolu Kardiyol Derg 2012; 12: 97-101)