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    A RECENT GENERALIZATION OF COFINITELY INJECTIVE MODULES
    (Honam Mathematical Soc, 2023) Sozen, Esra Ozturk
    Let R be an associative ring with identity and M be a left R-module. In this paper, we define modules that have the property (8 CE) ((8-CEE)), these are modules that have a 8-supplement (ample 8 supplements) in every cofinite extension which are generalized version of modules that have the properties (CE) and (CEE) introduced in [6] and so a generalization of Zoschinger's modules with the properties (E) and (EE) given in [23]. We investigate various properties of these modules along with examples. In particular we prove these: (1) a module M has the property (8-CEE) if and only if every submodule of M has the property (8 -CE); (2) direct summands of a module that has the property (8 -CE) also have the property (8 -CE); (3) each factor module of a module that has the property (8 -CE) also has the property (8 -CE) under a special condition; (4) every module with composition series has the property (8 CE); (5) over a 8 -V-ring a module M has the property (8 -CE) if and only if M is cofinitely injective; (6) a ring R is 8-semiperfect if and only if every left R-module has the property (8 -CE).
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    Algebraic approach to various chemical structures with new Banhatti coindices
    (Taylor & Francis Ltd, 2024) Sozen, Esra Ozturk; Eryasar, Elif
    Topological coindices are the numeric values, obtained by the complement graph of a molecular structure, which is used in Quantitative Structure Property/Activity Relationship (QSPR/QSAR) studies to evaluate the physicochemical and biological properties of compounds. In this article, we introduce new distance-based topological indices calculated with the CoM-polynomial approach. We present an application about the compatibility of these indices with some drugs that are candidates for use in the treatment of COVID-19 with QSPR analysis.
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    An Algebraic Approach to Calculate Some Topological Coindices and QSPR Analysis of Some Novel Drugs Used in the Treatment of Breast Cancer
    (Taylor & Francis Ltd, 2024) Sozen, Esra Ozturk; Eryasar, Elif
    Breast cancer is one of the most leading deadly diseases in the world whose ranks first among all oncological diseases in women and it is the second spearheading reason of cancer deadness after lung cancer in the United States. Researchers from all over the world are working for finding better ways for preventing, identifying, and treating breast cancer. Topological indices are the functions generating a numerical value from the molecular graph of compounds and they are also a useful tool to estimate the pyhsicochemical and biological properties of molecules in the quantitative structure-property (activity) relationship (QSPR/QSAR) studies. In this paper, some drugs are studied which are used for the treatment of breast cancer. CoM-polynomials based on degree are occurred for chemical graphs of these drugs and the values of some variable topological coindices are calculated via these polynomials. The results obtained by regression analysis show that the correlations of the chosen coindices with the physicochemical properties of the determined drugs are good even strong for some of them. The QSPR models are constructed using the curvilinear regression method with topological coindices.
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    Computing degree based topological indices of algebraic hypergraphs
    (Cell Press, 2024) Alali, Amal S.; Sozen, Esra Ozturk; Abdioglu, Cihat; Ali, Shakir; Eryasar, Elif
    Topological indices are numerical parameters that indicate the topology of graphs or hypergraphs. A hypergraph H = (V (H), E(H)) consists of a vertex set V (H) and an edge set E(H), where each edge e is an element of E(H) is a subset of V(H) with at least two elements. In this paper, our main aim is to introduce a general hypergraph structure for the prime ideal sum (PIS)- graph of a commutative ring. The prime ideal sum hypergraph of a ring R is a hypergraph whose vertices are all non-trivial ideals of R and a subset of vertices E, with at least two elements is a hyperedge whenever I + J is a prime ideal of R for each non-trivial ideal I, J in E, and E, is maximal with respect to this property. Moreover, we also compute some degree-based topological indices (first and second Zagreb indices, forgotten topological index, harmonic index, Randic index, Sombor index) for these hypergraphs. In particular, we describe some degree-based topological indices for the newly defined algebraic hypergraph based on prime ideal sum for Z(n) where n = p(alpha), pq, p(2)q, p(2)q(2), pqr, p(3)q, p(2)qr, pqrs for the distinct primes p, q, r and s.
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    Forgotten Topological and Wiener Indices of Prime Ideal Sum Graph of Zn
    (Bentham Science Publ Ltd, 2024) Sozen, Esra Ozturk; Eryasar, Elif; Abdioglu, Cihat
    Background: Chemical graph theory is a sub-branch of mathematical chemistry, assuming each atom of a molecule is a vertex and each bond between atoms as an edge. Objective: Owing to this theory, it is possible to avoid the difficulties of chemical analysis because many of the chemical properties of molecules can be determined and analyzed via topological indices. Due to these parameters, it is possible to determine the physicochemical properties, biological activities, environmental behaviours and spectral properties of molecules. Nowadays, studies on the zero divisor graph of Z(n) via topological indices is a trending field in spectral graph theory. Methods: For a commutative ring R with identity, the prime ideal sum graph of R is a graph whose vertices are nonzero proper ideals of R and two distinctvertices I and J are adjacent if and only if I+J is a prime ideal of R. Results: In this study the forgotten topological index and Wiener index of the prime ideal sum graph of Z(n) are calculated for n=p(alpha), pq, p(2)q, p(2)q(2), pqr, p(3)q, p(2)qr, pqrs where p,q,r and s are distinct primes and a Sage math code is developed for designing graph and computing the indices. Conclusion: In the light of this study, it is possible to handle the other topological descriptors for computing and developing new algorithms for next studies and to study some spectrum and graph energies of certain finite rings with respect to PIS-graph easily.
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    ON A GENERALIZATION OF ?-CO-COATOMICALLY SUPPLEMENTED MODULES
    (Honam Mathematical Soc, 2023) Eryilmaz, Figen; Sozen, Esra Ozturk
    In this paper, we define circle plus delta-co-coatomically supplemented and co-coatomically 6-semiperfect modules as a strongly notion of circle plus-co-coatomically supplemented and co-coatomically semiperfect modules with the help of Zhou's radical. We say that a module A is circle plus delta-co-coatomically supplemented if each co-coatomic submodule of A has a 6-supplement in A which is a direct summand of A. And a module A is co-coatomically 6-semiperfect if each coatomic factor module of A has a projective 6-cover. Also we define co-coatomically amply 6-supplemented modules and we examined the basic properties of these modules. Further-more, we give a ring characterization for our modules. In particular, a ring R is 6-semiperfect if and only if each free R-module is co-coatomically 6-semiperfect.
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    ON COFINITELY CLOSED WEAK δ-SUPPLEMENTED MODULES
    (Honam Mathematical Soc, 2020) Sozen, Esra Ozturk
    A module M is called cofinitely closed weak delta-supplemented (briefly delta-ccws-module) if for any cofinite closed submodule N of M has a weak delta-supplement in M: In this paper we investigate the basic properties of delta-ccws modules. In the light of this study, we can list the main facts obtained as following: (1) Any cofinite closed direct summand of a delta-ccws module is also a delta-ccws module; (2) Let R be a left delta-V-ring. Then R is a delta-ccws module iff R is a ccws-module iff R is extending; (3) Any nonsingular homomorphic image of a delta-ccws-module is also a delta-ccws-module; (4) We characterize nonsingular delta-V-rings in which all nonsingular modules are delta-ccws.
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    On δss-perfect modules
    (Univ Nis, Fac Sci Math, 2024) Sozen, Esra Ozturk
    After the definitions of perfect and semiperfect rings, the transportation of them to perfect and semiperfect modules is a significant creation for new characterizations of supplemented modules and the other modified versions of them. Inspired by this idea, we aim to create a route from delta(ss)-perfect rings to delta(ss)-perfect modules. A module W is said to be delta(ss)-perfect if each factor module is of a projective delta(ss)-cover. Owing to this goal, we obtain new relations for projective (amply) delta(ss)-supplemented and delta(ss)-lifting modules. Also, we present various characterization theorems for a (projective) module to be delta(ss)-perfect.
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    ON ⊕-S88-SUPPLEMENTED MODULES
    (Publications L Institut Mathematique Matematicki, 2022) Sozen, Esra Ozturk
    A module M is called E9-delta 88-supplemented if every submodule X of M has a delta 88-supplement Y in M which is a direct summand of M such that X + Y = M and X n Y Soco(Y) where Soco(Y) is the sum of simple and delta-small submodules of Y and M = Y E9 Y ' for some Y ' M. Moreover, M is called a completely E9-delta 88-supplemented module if every direct summand of M is E9-delta 88-supplemented. Thus, we present two new types of algebraic structures which are stronger than delta-D11 and delta-D+11-modules, respectively. In this paper we investigate basic properties, decompositions and ring characterizations of these modules.
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    QSPR Analysis of Some Drug Candidates Investigated for COVID-19 via New Topological Coindices
    (Taylor & Francis Ltd, 2024) Sozen, Esra Ozturk; Eryasar, Elif
    The COVID-19 outbreak has appeared as a matchless global threat against all humanity. Even the most developed countries have been shocked by the adversities of the COVID-19 pandemic affecting social life, especially human health. All over the world, researchers still have been studying to develop new medicines the combat outbreak. A topological index can be thought of as the conversion of a chemical structure to a real number. Topological indices are often used to provide information about the physicochemical properties and biological properties of molecules. Topological coindices are the numeric values, obtained by the complement graph of a molecular structure, which is used in Quantitative Structure Property/Activity Relationship (QSPR/QSAR) studies to evaluate the physicochemical and biological properties of compounds. In this study, we construct some new topological coindices and define the concept of CoNM-polynomial. Owing to these polynomials we pass the difficulty of calculating the topological coindices. The computing process is done for the molecular graph structure of fixed analogs of Lopinavir, Favipiravir and Ritonavir. Afterward, obtained values are evaluated in QSPR modeling via linear and quadratic regression analysis to examine some physicochemical properties of the analog medicines such as enthalpy of vaporization (E), flash point (FP), molar refractivity (MR), polarizability (P), surface tension (T), molar volume (MV).
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    Some Variations of δ-Supplemented Modules with Regard to a Hereditary Torsion Theory
    (Wiley, 2023) Tian, Jian; Sozen, Esra Ozturk; Hamzekolaee, Ali Reza Moniri
    In present work, we describe and investigate torsion theoretic versions of delta-supplemented modules via a hereditary torsion theory tau. With this aim, first, we define delta(tau)-small submodules. On this basis, the concepts of delta tau-lifting modules, delta(tau)-supplemented modules, and amply delta(tau)-supplemented modules and their fundamental properties are given, respectively. Furthermore, we present delta(tau)-semiperfect modules and give a characterization for them via (amply) delta(tau)-supplemented modules. Even we supply binary relations between these new module classes.