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dc.contributor.authorM. Ali Öztürk
dc.contributor.authorYoung Bae Jun
dc.date.accessioned23.07.201910:49:13
dc.date.accessioned2019-07-23T16:20:27Z
dc.date.available23.07.201910:49:13
dc.date.available2019-07-23T16:20:27Z
dc.date.issued2001
dc.identifier.issn1300-0098
dc.identifier.urihttp://www.trdizin.gov.tr/publication/paper/detail/TXpNMU56azU=
dc.identifier.urihttps://hdl.handle.net/20.500.12418/1233
dc.description.abstractThe aim of this paper is to study the properities of the extended centroid of the prime $\Gamma$-rings. Main results are the following theorems: (1) Let M be a simple $\Gamma$-ring with unity. Suppose that for some a$\neq$0 in M we have $a_{\gamma1}x_{\gamma2}a\beta1y\beta2a$ = $a\beta1y\beta2a_{\gamma1}x_{\gamma2}a$ for all x,y $\in$ M and $\gamma1,\gamma2,\beta1,\beta2\in\Gamma$. Then M is isomorphic onto the $\Gamma$-ring $D_{n,m}$, where $D_{n,m}$ is the additive abelian group of all rectangular matrices of type n x m over a division ring D and $\Gamma$ is a nonzero subgroup of the additive abelian group of all rectangular matrices of type m x n over a division ring D. Furthermore M is the $\Gamma$-ring of all n x n matrices over the field $C_{\Gamma}$. (2) Let M be a prime $\Gamma$-ring and $C_{\Gamma}$ the extended centroid of M. If a and b are non-zero elements in S = $M\Gamma C_{\Gamma}$ such that $q\gamma1x\gamma2\beta1y\beta2q$ =$q\beta1y\beta2q\gamma1x\gamma2q$ for all x $in$ M and $\beta,\gamma\in\Gamma$, then a and b are $C_{\Gamma}$-dependent. (3) Let M be prime $\Gamma$-ring, Q quotient $\Gamma$-ring of M and $C_{\Gamma}$ the extended centroid of M. If q is non-zero element in Q such that $q\gamma1x\gamma2q\beta1y\beta2q$ = $q\beta1y\beta2q\gamma1x\gamma2q$ for all x,y $\in$ M, $\gamma1,\gamma2,\beta1,\beta2\in\Gamma$ then S is a primitive $\Gamma$-ring with minimal right ( left ) ideal such that e$\Gamma$S, where e is idempotent and $C_{\Gamma}\Gamma e$ is the commuting ring of S on e$\Gamma$S.en_US
dc.description.abstractThe aim of this paper is to study the properities of the extended centroid of the prime $\Gamma$-rings. Main results are the following theorems: (1) Let M be a simple $\Gamma$-ring with unity. Suppose that for some a$\neq$0 in M we have $a_{\gamma1}x_{\gamma2}a\beta1y\beta2a$ = $a\beta1y\beta2a_{\gamma1}x_{\gamma2}a$ for all x,y $\in$ M and $\gamma1,\gamma2,\beta1,\beta2\in\Gamma$. Then M is isomorphic onto the $\Gamma$-ring $D_{n,m}$, where $D_{n,m}$ is the additive abelian group of all rectangular matrices of type n x m over a division ring D and $\Gamma$ is a nonzero subgroup of the additive abelian group of all rectangular matrices of type m x n over a division ring D. Furthermore M is the $\Gamma$-ring of all n x n matrices over the field $C_{\Gamma}$. (2) Let M be a prime $\Gamma$-ring and $C_{\Gamma}$ the extended centroid of M. If a and b are non-zero elements in S = $M\Gamma C_{\Gamma}$ such that $q\gamma1x\gamma2\beta1y\beta2q$ =$q\beta1y\beta2q\gamma1x\gamma2q$ for all x $in$ M and $\beta,\gamma\in\Gamma$, then a and b are $C_{\Gamma}$-dependent. (3) Let M be prime $\Gamma$-ring, Q quotient $\Gamma$-ring of M and $C_{\Gamma}$ the extended centroid of M. If q is non-zero element in Q such that $q\gamma1x\gamma2q\beta1y\beta2q$ = $q\beta1y\beta2q\gamma1x\gamma2q$ for all x,y $\in$ M, $\gamma1,\gamma2,\beta1,\beta2\in\Gamma$ then S is a primitive $\Gamma$-ring with minimal right ( left ) ideal such that e$\Gamma$S, where e is idempotent and $C_{\Gamma}\Gamma e$ is the commuting ring of S on e$\Gamma$S.en_US
dc.language.isoengen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectMatematiken_US
dc.titleOn the centroid of the prime gamma rings IIen_US
dc.typeotheren_US
dc.relation.journalTurkish Journal of Mathematicsen_US
dc.contributor.departmentSivas Cumhuriyet Üniversitesien_US
dc.identifier.volume25en_US
dc.identifier.issue3en_US
dc.identifier.endpage377en_US
dc.identifier.startpage367en_US
dc.relation.publicationcategoryDiğeren_US]


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