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Regularity of the generalized centroid of semi-prime gamma rings

Young Bae Jun|Mehmet Ali Ozturk
대한수학회 (The Korean Mathematical Society)|2004.04|대한수학회논문집 (Communications of the KMS)|제19권 제2호|pp. 233-242

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Abstract

The aim of this note is to study properties of thegeneralized centroid of the semi-prime gamma rings. Main resultsare the following theorems: (1) Let M be a semi-primeGamma-ring and Q a quotient Gamma-ring of M. If W is anon-zero submodule of the right(left) M-module Q, thenWGamma W neq 0. Furthermore Q is a semi-prime Gamma-ring.(2) Let M be a semi-prime Gamma-ring and C_{Gamma} thegeneralized centroid of M. Then C_{Gamma} is a regularGamma-ring. (3) Let M be a semi-prime Gamma-ring andC_{Gamma} the extended centroid of M. If C_{Gamma} is aGamma-field, then the Gamma-ring M is a primeGamma-ring.

참고문헌 (8)

  1. "On the Gamma-ring of Nobusawa", 18(3), pp.411~ (1966)
  2. "On prime gamma rings", 75(1), pp.185~ (1978)
  3. "On the theory of simple Gamma -rings", 16, pp.65~ (1969)
  4. "Prime rings satisfying a generalized polynomial identity", 12, pp.576~ (1969)
  5. "On a generalization of the ring theory", 1, pp.81~ (1964)
  6. "On the centroid of the prime gamma rings", 15(3), pp.469~479 (2000)
  7. "On the centroid of the prime gamma rings II", 25, pp.367~377 (2001)
  8. "Symmetric bi-derivation on prime gamma rings", 3(2), pp.273~281 (2000)

관련 논문AI추천

Modules over the generalized centroid of semi-prime Gamma ringsHasret Yazarl\i, Mehmet Al$\dot{\mbox{\sc i}}$ \대한수학회 · 대한수학회보2007 · 제44권 제2호Symmetric bi-$\left( \sigma ,\tau \right) $ derivations of prime and semi prime gamma ringsMustafa A, Sahin Ceran대한수학회 · 대한수학회보2006 · 제43권 제1호Permuting Tri-Derivations in Prime and Semi-Prime Gamma RingsDuran zden, Mehmet Ali ztrk, Young Bae Jun경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2006 · 제46권 제2호On prime Gamma-near-rings with derivationMehmet Ali Ozturk, Mustafa Ucckun, Young Bae Jun대한수학회 · 대한수학회논문집2004 · 제19권 제3호On prime and semiprime rings with permuting 3-derivations박규홍, 정용수대한수학회 · 대한수학회보2007 · 제44권 제4호On generalized $(\a, \b)$-derivations andcommutativity in prime rings박규홍, 정용수대한수학회 · 대한수학회보2006 · 제43권 제1호

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