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RISS 인기검색어
- 검색키워드
- 저자 : Buyukasik, Kenan (검색결과 6 건)
- 무료
- 기관 내 무료
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RINGS AND MODULES CHARACTERIZED BY OPPOSITES OF FP-INJECTIVITY
Buyukasik, EngIn,Kafkas-DemIrcI, GIzem Korean Mathematical Society 2019 대한수학회보 Vol.56 No.2
Let R be a ring with unity. Given modules $M_R$ and $_RN$, $M_R$ is said to be absolutely $_RN$-pure if $M{\otimes}N{\rightarrow}L{\otimes}N$ is a monomorphism for every extension $L_R$ of $M_R$. For a module $M_R$, the subpurity domain of $M_R$ is defined to be the collection of all modules $_RN$ such that $M_R$ is absolutely $_RN$-pure. Clearly $M_R$ is absolutely $_RF$-pure for every flat module $_RF$, and that $M_R$ is FP-injective if the subpurity domain of M is the entire class of left modules. As an opposite of FP-injective modules, $M_R$ is said to be a test for flatness by subpurity (or t.f.b.s. for short) if its subpurity domain is as small as possible, namely, consisting of exactly the flat left modules. Every ring has a right t.f.b.s. module. $R_R$ is t.f.b.s. and every finitely generated right ideal is finitely presented if and only if R is right semihereditary. A domain R is $Pr{\ddot{u}}fer$ if and only if R is t.f.b.s. The rings whose simple right modules are t.f.b.s. or injective are completely characterized. Some necessary conditions for the rings whose right modules are t.f.b.s. or injective are obtained.
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ON ω-LOCAL MODULES AND Rad-SUPPLEMENTED MODULES
Buyukasik, Engin,Tribak, Rachid Korean Mathematical Society 2014 대한수학회지 Vol.51 No.5
All modules considered in this note are over associative commutative rings with an identity element. We show that a ${\omega}$-local module M is Rad-supplemented if and only if M/P(M) is a local module, where P(M) is the sum of all radical submodules of M. We prove that ${\omega}$-local nonsmall submodules of a cyclic Rad-supplemented module are again Rad-supplemented. It is shown that commutative Noetherian rings over which every w-local Rad-supplemented module is supplemented are Artinian. We also prove that if a finitely generated Rad-supplemented module is cyclic or multiplication, then it is amply Rad-supplemented. We conclude the paper with a characterization of finitely generated amply Rad-supplemented left modules over any ring (not necessarily commutative).
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Upper Gastrointestinal Tract Polyps: What Do We Know About Them?
Buyukasik, Kenan,Sevinc, Mert Mahsuni,Gunduz, Umut Riza,Ari, Aziz,Gurbulak, Bunyamin,Toros, Ahmet Burak,Bektas, Hasan Asian Pacific Journal of Cancer Prevention 2015 Asian Pacific journal of cancer prevention Vol.16 No.7
Background: This study aimed to evaluate upper gastrointestinal polyps detected during esophago-gastroduodenoscopy tests. Materials and Methods: We conducted a retrospective analysis on data regarding 55,987 upper gastrointestinal endoscopy tests performed at the endoscopy unit of Istanbul Education and Research Hospital between January 2006 and June 2012. Results: A total of 66 upper gastrointestinal polyps from 59 patients were analyzed. The most common clinical symptom was dyspepsia, observed in 41 cases (69.5%). The localizations of the polyps were as follows: 29 in the antrum (43.9%), 15 in the corpus (22.7%), 11 in the cardia (16.7%), 3 in the fundus (4.54%), 3 in the second portion of the duodenum (4.54%), 2 in the bulbus (3.03%) and 3 in the lower end of the esophagus (4.54%). Histopathological types of polyps included hyperplastic polyps (44) (66.7%), faveolar hyperplasia (8) (12.1%), fundic gland polyps (4) (6.06%), squamous cell polyps (4) (6.06%), hamartomatous polyps (3) (4.54%), and pyloric gland adenoma (3) (4.54%). Histopathological analysis of the gastric mucosa showed chronic atrophic gastritis in 30 cases (50.84%), HP infection in 33 cases (55.9%) and intestinal metaplasia in 19 cases (32.20%). In 3 cases with multiple polyps, adenocarcinoma was detected in hyperplastic polyps. Conclusions: Among polypoid lesions of the upper gastrointestinal tract, the most common histological type is hyperplastic polyps. Generally, HP infection is associated with chronic atrophic gastritis and intestinal metaplasia. The incidence of adenocarcinoma tends to be higher in patients with multiple hyperplastic polyps.
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CONEAT SUBMODULES AND CONEAT-FLAT MODULES
Buyukasik, Engin,Durgun, Yilmaz Korean Mathematical Society 2014 대한수학회지 Vol.51 No.6
A submodule N of a right R-module M is called coneat if for every simple right R-module S, any homomorphism $N{\rightarrow}S$ can be extended to a homomorphism $M{\rightarrow}S$. M is called coneat-flat if the kernel of any epimorphism $Y{\rightarrow}M{\rightarrow}0$ is coneat in Y. It is proven that (1) coneat submodules of any right R-module are coclosed if and only if R is right K-ring; (2) every right R-module is coneat-flat if and only if R is right V -ring; (3) coneat submodules of right injective modules are exactly the modules which have no maximal submodules if and only if R is right small ring. If R is commutative, then a module M is coneat-flat if and only if $M^+$ is m-injective. Every maximal left ideal of R is finitely generated if and only if every absolutely pure left R-module is m-injective. A commutative ring R is perfect if and only if every coneat-flat module is projective. We also study the rings over which coneat-flat and flat modules coincide.
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CONEAT SUBMODULES AND CONEAT-FLAT MODULES
Engin Buyukasik,Yilmaz Durugun 대한수학회 2014 대한수학회지 Vol.51 No.6
A submodule N of a right R-module M is called coneat if for every simple right R-module S, any homomorphism N → S can be extended to a homomorphism M → S. M is called coneat-flat if the kernel of any epimorphism Y → M → 0 is coneat in Y . It is proven that (1) coneat submodules of any right R-module are coclosed if and only if R is right K-ring; (2) every right R-module is coneat-flat if and only if R is right V -ring; (3) coneat submodules of right injective modules are exactly the modules which have no maximal submodules if and only if R is right small ring. If R is commutative, then a module M is coneat- flat if and only if M + is m-injective. Every maximal left ideal of R is finitely generated if and only if every absolutely pure left R-module is m- injective. A commutative ring R is perfect if and only if every coneat-flat module is projective. We also study the rings over which coneat-flat and flat modules coincide.
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Rings and modules characterized by opposites of FP-injectivity
Engin Buyukasik,Gizem Kafkas-Demirci 대한수학회 2019 대한수학회보 Vol.56 No.2
Let $R$ be a ring with unity. Given modules $M_R$ and $_RN$, $M_R$ is said to be absolutely $_RN$-pure if $M \otimes N \to L \otimes N$ is a monomorphism for every extension $L_R$ of $M_R$. For a module $M_R$, the subpurity domain of $M_R$ is defined to be the collection of all modules $_RN$ such that $M_R$ is absolutely $_RN$-pure. Clearly $M_R$ is absolutely $_RF$-pure for every flat module $_RF$, and that $M_R$ is FP-injective if the subpurity domain of $M$ is the entire class of left modules. As an opposite of FP-injective modules, $M_R$ is said to be a \emph{test for flatness by subpurity $($or t.f.b.s.~for short$)$} if its subpurity domain is as small as possible, namely, consisting of exactly the flat left modules. Every ring has a right $t.f.b.s.$~module. $R_R$ is t.f.b.s.~and every finitely generated right ideal is finitely presented if and only if $R$ is right semihereditary. A domain $R$ is Pr\"{u}fer if and only if $R$ is t.f.b.s. The rings whose simple right modules are t.f.b.s.~or injective are completely characterized. Some necessary conditions for the rings whose right modules are t.f.b.s.~or injective are obtained.
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