FUNDA TAŞDEMİR | Bozok University (original) (raw)

Papers by FUNDA TAŞDEMİR

Research paper thumbnail of On Binomial Double Sums with Fibonacci and Lucas numbers-I

Research paper thumbnail of Triple sums including Fibonacci numbers with three binomial coefficients

Notes on Number Theory and Discrete Mathematics, Mar 1, 2021

In this paper, we consider some triple sums that involve Fibonacci numbers with three binomial co... more In this paper, we consider some triple sums that involve Fibonacci numbers with three binomial coefficients. We chose the indices of Fibonacci numbers as linear combination of the summation indices. Moreover, various types of alternating analogues of them whose powers depend on the index or indices are computed. These sums are evaluated in nice multiplication forms in terms of Fibonacci and Lucas numbers.

Research paper thumbnail of Equiprime N-ideals of Monogenic N-groups

Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics

There are many variants of primeness for near-rings generalizing prime rings. Amongst them are eq... more There are many variants of primeness for near-rings generalizing prime rings. Amongst them are equiprime, 3-prime and completely prime near-rings. Subsequently these notions were extended to N-ideals of N-groups. The authors investigate the relationships between the three mentioned generalizations subject to weak commutativity requirements. For example, let Γ be an N-group with P an N-ideal of Γ. If N is right permutable, then P is a completely prime N-ideal if and only if P is a 3-prime N-ideal; if N is a medial near-ring, then P is a completely prime ideal if and only if P is a 3-prime N-ideal and if N is left-permutable, then P is equiprime if and only if P is a completely prime N-ideal.

Research paper thumbnail of New binomial double sums with products op fibonacci and lucas numbers

Utilitas Mathematica Publishing Inc., 2019

Research paper thumbnail of Equiprime N-ideals of Monogenic N-groups ABSTRACT | FULL TEXT

Hacettepe Journal of Mathematics and Statistics, 2011

In this paper we introduce the notion of equiprime N-ideals where N is a near-ring. We consider t... more In this paper we introduce the notion of equiprime N-ideals where N is a near-ring. We consider the interconnections of equiprime, 3-prime and completely prime N-ideals of a monogenic N-group Γ. We show that if P is an equiprime N-ideal of Γ, then (P : Γ)N is an equiprime ideal of N, and that the converse holds when N is a right permutable near-ring and Γ is a monogenic N-group.

Research paper thumbnail of Applications of primeness in near rings to Malone trivial near rings

A ‘Malone trivial near-ring’ is a near-ring N for which there is a subset S⊆N∖{0} such that for a... more A ‘Malone trivial near-ring’ is a near-ring N for which there is a subset S⊆N∖{0} such that for all a,b∈N, ab=a if b∈S and ab=0 if b∉S. The authors study relationships between such near-rings and near-rings satisfying properties of being right (left) permutable, medial, left (right) self-distributive, 3-prime and/or completely prime. Although not mentioned, it seems that they only consider the more restricted Malone trivial near-rings with S=N∖{0}.

Research paper thumbnail of Completely Equiprime Ideals of Near-Ring Modules

Karaelmas Science and Engineering Journal, 2018

In this study, the concept of completely equiprime N-ideal (ideal of near-ring modules) is introd... more In this study, the concept of completely equiprime N-ideal (ideal of near-ring modules) is introduced. Also the interconnections of completely equiprime, equiprime and completely prime N-ideals are considered. It is proved that if P is a completely equiprime ideal of an N-group (near-ring module) Γ , then (P: Γ ) is a completely equiprime ideal of a near-ring N. The converse relation does not hold in general, however we provide some additional conditions for the converse to be true. The connection between the concepts of completely equiprime N-ideal and IFP N-ideal is also observed.

Research paper thumbnail of ON P-3-PRIME AND P-c-PRIME IDEALS IN NEAR-RINGS

JP Journal of Algebra, Number Theory and Applications, 2019

Research paper thumbnail of Boole Yakın Halkalar ve Boole İdealler

Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2018

Bu çalışmada, Boole yakın halka kavramı yakın halkaların ideallerine genişletilerek Boole ideal k... more Bu çalışmada, Boole yakın halka kavramı yakın halkaların ideallerine genişletilerek Boole ideal kavramı tanımlanmıştır. Elde edilen yeni tanımla birlikte Boole idealler ile literatürdeki diğer yapılar arasındaki ilişkiler incelenmiştir. Her Boole idealin aynı zamanda bir IFP ideal olduğu ancak tersinin doğru olmadığı ispatlanmıştır. Yine, Boole yakın halkaların sıfırlayan ideallerinin de Boole ideal olduğu ispatlanmıştır. Ayrıca, kendisi Boole olmadığı halde Boole ideale sahip çeşitli yakın halkalar örnek olarak incelenmiştir. Son olarak, verilen bir Boole halkadan Boole yakın halka elde etme yöntemi ile bir Boole yakın halka elde edilmiştir.

Research paper thumbnail of Triple sums including Fibonacci numbers with three binomial coefficients

Notes on Number Theory and Discrete Mathematics

In this paper, we consider some triple sums that involve Fibonacci numbers with three binomial co... more In this paper, we consider some triple sums that involve Fibonacci numbers with three binomial coefficients. We chose the indices of Fibonacci numbers as linear combination of the summation indices. Moreover, various types of alternating analogues of them whose powers depend on the index or indices are computed. These sums are evaluated in nice multiplication forms in terms of Fibonacci and Lucas numbers.

Research paper thumbnail of Different prime N-ideals and IFP N-Ideals

Indian Journal of Pure and Applied Mathematics, 2013

Research paper thumbnail of On Binomial Double Sums with Fibonacci and Lucas numbers-I

Research paper thumbnail of Triple sums including Fibonacci numbers with three binomial coefficients

Notes on Number Theory and Discrete Mathematics, Mar 1, 2021

In this paper, we consider some triple sums that involve Fibonacci numbers with three binomial co... more In this paper, we consider some triple sums that involve Fibonacci numbers with three binomial coefficients. We chose the indices of Fibonacci numbers as linear combination of the summation indices. Moreover, various types of alternating analogues of them whose powers depend on the index or indices are computed. These sums are evaluated in nice multiplication forms in terms of Fibonacci and Lucas numbers.

Research paper thumbnail of Equiprime N-ideals of Monogenic N-groups

Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics

There are many variants of primeness for near-rings generalizing prime rings. Amongst them are eq... more There are many variants of primeness for near-rings generalizing prime rings. Amongst them are equiprime, 3-prime and completely prime near-rings. Subsequently these notions were extended to N-ideals of N-groups. The authors investigate the relationships between the three mentioned generalizations subject to weak commutativity requirements. For example, let Γ be an N-group with P an N-ideal of Γ. If N is right permutable, then P is a completely prime N-ideal if and only if P is a 3-prime N-ideal; if N is a medial near-ring, then P is a completely prime ideal if and only if P is a 3-prime N-ideal and if N is left-permutable, then P is equiprime if and only if P is a completely prime N-ideal.

Research paper thumbnail of New binomial double sums with products op fibonacci and lucas numbers

Utilitas Mathematica Publishing Inc., 2019

Research paper thumbnail of Equiprime N-ideals of Monogenic N-groups ABSTRACT | FULL TEXT

Hacettepe Journal of Mathematics and Statistics, 2011

In this paper we introduce the notion of equiprime N-ideals where N is a near-ring. We consider t... more In this paper we introduce the notion of equiprime N-ideals where N is a near-ring. We consider the interconnections of equiprime, 3-prime and completely prime N-ideals of a monogenic N-group Γ. We show that if P is an equiprime N-ideal of Γ, then (P : Γ)N is an equiprime ideal of N, and that the converse holds when N is a right permutable near-ring and Γ is a monogenic N-group.

Research paper thumbnail of Applications of primeness in near rings to Malone trivial near rings

A ‘Malone trivial near-ring’ is a near-ring N for which there is a subset S⊆N∖{0} such that for a... more A ‘Malone trivial near-ring’ is a near-ring N for which there is a subset S⊆N∖{0} such that for all a,b∈N, ab=a if b∈S and ab=0 if b∉S. The authors study relationships between such near-rings and near-rings satisfying properties of being right (left) permutable, medial, left (right) self-distributive, 3-prime and/or completely prime. Although not mentioned, it seems that they only consider the more restricted Malone trivial near-rings with S=N∖{0}.

Research paper thumbnail of Completely Equiprime Ideals of Near-Ring Modules

Karaelmas Science and Engineering Journal, 2018

In this study, the concept of completely equiprime N-ideal (ideal of near-ring modules) is introd... more In this study, the concept of completely equiprime N-ideal (ideal of near-ring modules) is introduced. Also the interconnections of completely equiprime, equiprime and completely prime N-ideals are considered. It is proved that if P is a completely equiprime ideal of an N-group (near-ring module) Γ , then (P: Γ ) is a completely equiprime ideal of a near-ring N. The converse relation does not hold in general, however we provide some additional conditions for the converse to be true. The connection between the concepts of completely equiprime N-ideal and IFP N-ideal is also observed.

Research paper thumbnail of ON P-3-PRIME AND P-c-PRIME IDEALS IN NEAR-RINGS

JP Journal of Algebra, Number Theory and Applications, 2019

Research paper thumbnail of Boole Yakın Halkalar ve Boole İdealler

Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2018

Bu çalışmada, Boole yakın halka kavramı yakın halkaların ideallerine genişletilerek Boole ideal k... more Bu çalışmada, Boole yakın halka kavramı yakın halkaların ideallerine genişletilerek Boole ideal kavramı tanımlanmıştır. Elde edilen yeni tanımla birlikte Boole idealler ile literatürdeki diğer yapılar arasındaki ilişkiler incelenmiştir. Her Boole idealin aynı zamanda bir IFP ideal olduğu ancak tersinin doğru olmadığı ispatlanmıştır. Yine, Boole yakın halkaların sıfırlayan ideallerinin de Boole ideal olduğu ispatlanmıştır. Ayrıca, kendisi Boole olmadığı halde Boole ideale sahip çeşitli yakın halkalar örnek olarak incelenmiştir. Son olarak, verilen bir Boole halkadan Boole yakın halka elde etme yöntemi ile bir Boole yakın halka elde edilmiştir.

Research paper thumbnail of Triple sums including Fibonacci numbers with three binomial coefficients

Notes on Number Theory and Discrete Mathematics

In this paper, we consider some triple sums that involve Fibonacci numbers with three binomial co... more In this paper, we consider some triple sums that involve Fibonacci numbers with three binomial coefficients. We chose the indices of Fibonacci numbers as linear combination of the summation indices. Moreover, various types of alternating analogues of them whose powers depend on the index or indices are computed. These sums are evaluated in nice multiplication forms in terms of Fibonacci and Lucas numbers.

Research paper thumbnail of Different prime N-ideals and IFP N-Ideals

Indian Journal of Pure and Applied Mathematics, 2013