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A Class of Finsler Metrics with Almost Vanishing H- and ?-curvatures
(Springer Basel Ag, 2021) Gabrani, Mehran; Rezaei, Bahman; Sevim, Esra Sengelen
In this paper, we study Xi -curvature and H-curvature of a special class of Finsler metrics called general (alpha,beta)-metrics. We prove that every general (alpha,beta)-metric of almost vanishing H-curvature is of almost vanishing Xi -curvature under certain conditions. Moreover, we study such Finsler metric with vanishing Xi -curvature and its interaction to the flag curvature.
A Submodule-Based Zero Divisor Graph for Modules
(Tarbiat Modares Univ, 2019) Babaei, Sakineh; Payrovi, Shiroyeh; Sevim, Esra Sengelen
Let R be a commutative ring with identity and M be an R-module. The zero divisor graph of M is denoted by Gamma(M). In this study, we are going to generalize the zero divisor graph Gamma(M) to submodule-based zero divisor graph Gamma(M, N) by replacing elements whose product is zero with elements whose product is in some submodule N of M. The main objective of this paper is to study the interplay of the properties of submodule N and the properties of Gamma(M, N).
b-Symbol Distance Distribution of Repeated-Root Cyclic Codes
(Springer, 2018) Mostafanasab, Hojjat; Sevim, Esra Sengelen
Symbol-pair codes, introduced by Cassuto and Blaum (Proc IEEE Int Symp Inf Theory, 988-992, 2010 [1]), have been raised for symbol-pair read channels. This new idea is motivated by the limitations of the reading process in high-density data storage technologies. Yaakobi et al. (IEEE Trans Inf Theory 62(4):1541-1551, 2016 [8]) introduced codes for b-symbol read channels, where the read operation is performed as a consecutive sequence of b > 2 symbols. In this paper, we come up with a method to compute the b-symbol-pair distance of two n-tuples, where n is a positive integer. Also, we deal with the b-symbol-pair distances of some kind of cyclic codes of length p(e) over F-pm.
General spherically symmetric Finsler metrics with constant Ricci and flag curvature
(Elsevier, 2021) Gabrani, Mehran; Rezaei, Bahman; Sevim, Esra Sengelen
In this paper, we investigate the flag curvature of a special class of Finsler metrics called general spherically symmetric Finsler metrics, which are defined by a Euclidean metric and two related 1-forms. We find equations to characterize the class of metrics with constant Ricci curvature (tensor) and constant flag curvature. Moreover, we study general spherically symmetric Finsler metrics with the vanishing non-Riemannian quantity chi-curvature. In particular, we construct some new projectively flat Finsler metrics of constant flag curvature. (C) 2021 Elsevier B.V. All rights reserved.
LOCALLY S-PRIME IDEALS
(Publ House Bulgarian Acad Sci, 2020) Arabaci, Tarik; Sevim, Esra Sengelen
Let R be a commutative ring and S be a multiplicatively closed subset of R. Lambda proper ideal P of R is called locally S-prime if P-S is a prime ideal of R-S. It is shown that, P is a locally S-prime ideal if and only if whenever P boolean AND S = ? and if ab is an element of P for some a, b is an element of R, then there exists s is an element of S such that sa is an element of P or sb is an element of P. As a consequence of this fact and well-known properties of prime ideals we obtain some properties of these ideals. Also, all multiplicatively closed subsets S of R that an ideal can be locally S-prime are characterised. Finally, these ideals are studied in an S-Noetherian ring.
Multiplication Modules and Principal Elements of Modules Over Noncommutative Rings
(Util Math Publ Inc, 2012) Sevim, Esra Sengelen
By considering the notion of multiplication modules over a noncommutative ring with identity, first we introduce the notion of the product of two submodules of such modules. Then we use this notion to characterize the prime submodules of a multiplication module. Moreover we define some principal elements of modules over a noncommutative ring and we prove theorems related to principal elements.
ON A CLASS OF FINSLER METRICS OF QUADRATIC WEYL CURVATURE
(Tohoku University, 2023) Gabrani, Mehran; Sevim, Esra Sengelen; Shen, Zhongmin
The class of warped product manifolds plays an important role in differential geometry and physics. In this paper, we shall study product manifolds R x ?????? with Finsler metrics arising from warped product structure. We give an equivalent condition for those metrics to be of quadratic Weyl curvature.
ON A CLASS OF RICCI-FLAT DOUGLAS METRICS
(World Scientific Publ Co Pte Ltd, 2012) Sevim, Esra Sengelen; Shen, Zhongmin; Zhao, Lili
In this paper, we study a special class of Finsler metrics which are defined by a Riemannian metric and a 1-form on a manifold. We find equations that characterize Ricci-flat Douglas metrics among this class.
On Einstein Finsler metrics
(World Scientific Publ Co Pte Ltd, 2021) Ulgen, Semail; Sevim, Esra Sengelen; Hacinliyan, Irma
In this paper, we study Finsler metrics expressed in terms of a Riemannian metric, a 1-form, and its norm and find equations with sufficient conditions for such Finsler metrics to become Ricci-flat. Using certain transformations, we show that these equations have solutions and lead to the construction of a large and special class of Einstein metrics.
On Finsler Warped Product Metrics with Special Curvatures Properties
(Springernature, 2022) Gabrani, Mehran; Rezaei, Bahman; Sevim, Esra Sengelen
In this paper, we study a class of Finsler metrics called Finsler warped product metrics. We prove that every Finsler warped product metric is of isotropic E-curvature if and only if it is of isotropic S-curvature. Moreover, we prove that if the metric is of Douglas type and has isotropic S-curvature, then it must be Randers metric or Berwald metric.
On Landsberg Warped Product Metrics
(B Verkin Inst Low Temperature Physics & Engineering Nas Ukraine, 2021) Gabrani, Mehran; Rezaei, Bahman; Sevim, Esra Sengelen
In this paper, we discuss a class of Finsler metrics which are called Finsler warped product metrics. These metrics have been studied by Chen-Shen-Zhao, 2018. Basically, we study the Berwald curvature of Finsler warped product metrics. Also, we characterize the Finsler warped product metrics of isotropic Berwald curvature, then we obtain that they are Randers metrics (Theorem 1.2). Moreover, we consider an important problem which is unicorn problem in Finsler geometry for the class of Finsler metrics. In fact, we get the answer of the crucial question of this study that whether or not such a Landsberg Finsler warped product metric is a Berwald metric (Theorem 1.3).
ON n-PRIME IDEALS
(Univ Politehnica Bucharest, Sci Bull, 2018) Sevim, Esra Sengelen; Koc, Suat
In this article, we introduce an intermediate classes of ideals between prime and quasi primary ideals, denoted by n-prime, and we focus on some properties of n-prime ideals. Moreover, we defined a topology on the set of all n-prime ideals such that we examine the topological concepts, irreducibility, connectedness, and seperation axioms.
On projective invariants of general spherically symmetric Finsler spaces in Rn
(Elsevier, 2022) Gabrani, Mehran; Rezaei, Bahman; Sevim, Esra Sengelen
In this paper we discuss projective invariants of general spherically symmetric Finsler metrics in R-n. We obtain the necessary and sufficient conditions for the metrics to be projectively Ricci flat, Weyl and W-quadratic types. In particular, we use the spray theory to give a short proof of the well-known theorem, that is, Finsler manifold is of scalar flag curvature if and only if F is Weyl metric . Therefore, considering the technique of the proof, we obtain a necessary and sufficient condition for the metrics of scalar flag curvature to be Weyl metric. Also, under a certain condition, we prove that projectively Ricci flat general spherically symmetric metrics coincide with the Douglas type metric.(c) 2022 Elsevier B.V. All rights reserved.
On Some Ricci Curvature Tensors in Finsler Geometry
(Springer Basel Ag, 2023) Sevim, Esra Sengelen; Shen, Zhongmin; Ulgen, Semail
In this paper, we discuss several Ricci curvature tensors and their relationship with the Ricci curvature and some non-Riemannian quantities. By these Ricci curvature tensors, we shall have a better understanding on the non-Riemannian quantities.
On strongly Ricci-Quadratic Finsler Metrics
(Springer, 2023) Sevim, Esra Sengelen; Shen, Zhongmin; Ulgen, Semail
Finsler metrics being Ricci-quadratic is a non-Riemannian condition since the Ricci curvature (tensor) is always Ricci-quadratic for Riemannian metrics. In this paper, we introduce the notion of strongly Ricci-quadratic Finsler metrics. We classify strongly Ricci-quadratic Randers metrics expressed in a navigation form.
On the Annihilator Submodules and the Annihilator Essential Graph
(Springer Singapore Pte Ltd, 2019) Babaei, Sakineh; Payrovi, Shiroyeh; Sevim, Esra Sengelen
Let R be a commutative ring and let M be an R-module. For a is an element of R, Ann(M)(a) = {m is an element of M : am = 0} is said to be an annihilator submodule of M. In this paper, we study the property of being prime or essential for annihilator submodules of M. Also, we introduce the annihilator essential graph of equivalence classes of zero divisors of M, AE(R)(M), which is constructed from classes of zero divisors, determined by annihilator submodules of M and distinct vertices [a] and [b] are adjacent whenever Ann(M)(a) + Ann(M)(b) is an essential submodule of M. Among other things, we determine when AE(R)(M) is a connected graph, a star graph, or a complete graph. We compare the clique number of AE(R)(M) and the cardinal of m -Ass(R)(M).
On the compressed essential graph of a commutative ring
(Belgian Mathematical Soc Triomphe, 2019) Payrovi, Shiroyeh; Babaei, Sakineh; Sevim, Esra Sengelen
Let R be a commutative ring. In this paper, we introduce and study the compressed essential graph of R, EG(E)(R). The compressed essential graph of R is a graph whose vertices are equivalence classes of non-zero zero-divisors of R and two distinct vertices [x] and [y] are adjacent if and only if ann(xy) is an essential ideal of R. It is shown if R is reduced, then EG(E)(R) = Gamma(E)(R), where Gamma(E)(R) denotes the compressed zero-divisor graph of R. Furthermore, for a non-reduced Noetherian ring R with 3 < vertical bar EG(E)(R)vertical bar < infinity, it is shown that EG(E)(R) = Gamma(E)(R) if and only if (i) Nil(R) = ann(Z(R)). (ii) Every non-zero element of Nil(R) is irreducible in Z(R).
Projectively Ricci-flat general (?, ?)-metrics
(Springer Heidelberg, 2024) Sevim, Esra Sengelen
In this paper, we study the projectively Ricci-flat general (alpha, beta)-metrics within to a spray framework and also bring out the rich variety of behaviour displayed by an important projective invariant. Projective Ricci curvature is one of the essential projective invariant in Finsler geometry which has been introduced by Z. Shen. The projective Ricci curvature is defined as Ricci curvature of a projective spray associated with a given spray G on M-n with a volume form dV on M-n.
Randers Metrics of Constant Scalar Curvature
(Canadian Mathematical Soc, 2013) Sevim, Esra Sengelen; Shen, Zhongmin
Randers metrics are a special class of Finsler metrics. Every Randers metric can be expressed in terms of a Riemannian metric and a vector field via Zermelo navigation. In this paper, we show that a Randers metric has constant scalar curvature if the Riemannian metric has constant scalar curvature and the vector field is homothetic.
S-Artinian rings and finitely S-cogenerated rings
(World Scientific Publ Co Pte Ltd, 2020) Sevim, Esra Sengelen; Tekir, Unsal; Koc, Suat
Let R be a commutative ring with nonzero identity and S subset of R be a multiplicatively closed subset. In this paper, we study S-Artinian rings and finitely S-cogenerated rings. A commutative ring R is said to be an S-Artinian ring if for each descending chain of ideals {In}(n is an element of N) of R, there exist s is an element of S and k is an element of N such that sI(k) subset of I-n for all n >= k. Also, R is called a finitely S-cogenerated ring if for each family of ideals {I alpha}(alpha)(is an element of Delta) of R, = where Delta is an index set, boolean AND(alpha is an element of Delta) I alpha implies = 0 implies s(boolean AND(alpha is an element of Delta), I alpha) = 0 for some s is an element of S and a finite subset Delta' subset of Delta. Moreover, we characterize some special rings such as Artinian rings and finitely cogenerated rings. Also, we extend many properties of Artinian rings and finitely cogenerated rings to S-Artinian rings and finitely S-cogenerated rings.

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