Author
Ünsal Tekir
Bio: Ünsal Tekir is an academic researcher from Marmara University. The author has contributed to research in topics: Commutative ring & Prime (order theory). The author has an hindex of 14, co-authored 97 publications receiving 609 citations.
Papers published on a yearly basis
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TL;DR: In this article, the concept of 2-absorbing primary ideal was introduced, which is a generalization of the primary ideal, and a proper ideal I of a commutative ring is called a 2 absorbing primary ideal of R if whenever a, b, c ∈ R and abc ∈ I,t henab ∈ √ I or ac ∈ ǫ I or bc ∈ Á or Á ∫ I,
Abstract: Let R be a commutative ring with 1 � . In this paper, we introduce the concept of 2-absorbing primary ideal which is a general- ization of primary ideal. A proper ideal I of R is called a 2-absorbing primary ideal of R if whenever a, b, c ∈ R and abc ∈ I ,t henab ∈ I or ac ∈ √ I or bc ∈ √ I. A number of results concerning 2-absorbing primary ideals and examples of 2-absorbing primary ideals are given.
107 citations
TL;DR: In this article, various properties of graded prime submodules and graded primary submodules of multiplication graded R-modules are discussed, and the graded radical of graded submodules is discussed.
Abstract: Let G be a multiplicative group. Let R be a G-graded commutative ring and M a G-graded R-module. Various properties of graded prime submodules and graded primary submodules of M are discussed. We have also discussed the graded radical of graded submodules of multiplication graded R-modules.
57 citations
TL;DR: In this paper, the concepts of S -prime submodules and S -torsion-free modules were introduced, which are generalizations of prime sub-modules and torsion free modules.
Abstract: In this study, we introduce the concepts of S -prime submodules and S -torsion-free modules, which are generalizations of prime submodules and torsion-free modules. Suppose S ⊆ R is a multiplicatively closed subset of a commutative ring R , and let M be a unital R -module. A submodule P of M with (P :R M) ∩ S = ∅ is called an S -prime submodule if there is an s ∈ S such that am ∈ P implies sa ∈ (P :R M) or sm ∈ P. Also, an R -module M is called S -torsion-free if ann(M) ∩ S = ∅ and there exists s ∈ S such that am = 0 implies sa = 0 or sm = 0 for each a ∈ R and m ∈ M. In addition to giving many properties of S -prime submodules, we characterize certain prime submodules in terms of S -prime submodules. Furthermore, using these concepts, we characterize some classical modules such as simple modules, S -Noetherian modules, and torsion-free modules.
38 citations
TL;DR: Weakly 2-absorbing primary ideal as mentioned in this paper is a generalization of weakly absorbing primary ideal, and it is defined as the ideal of a commutative ring with 1 6 0.
Abstract: Let R be a commutative ring with 1 6 0. In this paper, we introduce the concept of weakly 2-absorbing primary ideal which is a generalization of weakly 2-absorbing ideal. A proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever a,b,c ∈ R and 0 6 abc ∈ I, then ab ∈ I or ac ∈ √ I or bc ∈ √ I. A number of results concerning weakly 2-absorbing primary ideals and examples of weakly 2-absorbing primary ideals are given.
32 citations
TL;DR: In this article, the authors define a proper ideal I of R as an n-ideal if whenever ab ∈ I with a < √ 0, then b∈ I for every a, b ∈ R.
Abstract: In this paper, we present a new classes of ideals: called n-ideal. Let R be a commutative ring with nonzero identity. We define a proper ideal I of R as an n-ideal if whenever ab ∈ I with a < √ 0, then b ∈ I for every a, b ∈ R. We investigate some properties of n-ideals analogous with prime ideals. Also, we give many examples with regard to n-ideals.
31 citations
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TL;DR: In this paper, a text on rings, fields and algebras is intended for graduate students in mathematics, aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation.
Abstract: This text, drawn from the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-term course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semi-simple rings, Jacobson's theory of the radical representation theory of groups and algebras, prime and semi-prime rings, primitive and semi-primitive rings, division rings, ordered rings, local and semi-local rings, and perfect and semi-perfect rings. By aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation, the author has produced a text which is suitable not only for use in a graduate course, but also for self-study by other interested graduate students. Numerous exercises are also included. This graduate textbook on rings, fields and algebras is intended for graduate students in mathematics.
1,479 citations
393 citations
TL;DR: A system that absorbs air from the environment using carbon dioxide, oxygen and carbon monoxide values in ambient air and controls the operation of the ventilation system that gives fresh air to the environment is designed with fuzzy logic method to achieve the ideal ventilation level.
Abstract: The ventilation systems are inadequate, the increase in the amount of carbon dioxide and carbon monoxide in the inner environment can damage human health. In addition, obtaining the level of extern...
104 citations
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TL;DR: In this article, the Anderson-Badawi conjecture about weakly absorbing ideals and the Badawi-Yousefian conjecture on weakly 2-absorbing ideals were investigated.
Abstract: All rings are commutative with $1
eq0$. The purpose of this paper is to investigate the concept of weakly $n$-absorbing ideals generalizing weakly 2-absorbing ideals. We prove that over a $u$-ring $R$ the Anderson-Badawi's conjectures about $n$-absorbing ideals and the Badawi-Yousefian's question about weakly 2-absorbing ideals hold.
52 citations