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On QB-ideals of exchange rings

Huanyin Chen
대한수학회 (The Korean Mathematical Society)|2009.09|대한수학회보 (Bulletin of the KMS)|제46권 제5호|pp. 873-884

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참고문헌

키워드

annihilatorQB-idealexchange ringdiagonal reduction
주제분류수학

초록

We characterize QB-ideals of exchange rings by means of quasi-invertible elements and annihilators. Further, we prove that every 2×2 matrix over such ideals of a regular ring admits a diagonal reduction by quasi-inverse matrices. Prime exchange QB-rings are studied as well.

Abstract

We characterize QB-ideals of exchange rings by means of quasi-invertible elements and annihilators. Further, we prove that every 2×2 matrix over such ideals of a regular ring admits a diagonal reduction by quasi-inverse matrices. Prime exchange QB-rings are studied as well.

참고문헌 (10)

  1. P. Ara, "An infinite analogue of rings with stable rank one", J. Algebra, 230(2), pp.608~655 (2000)
  2. P. Ara, "Extensions and pullbacks in QB-rings", Algebr. Represent. Theory, 8(1), pp.75~97 (2005)
  3. H. Chen, "On exchange QB-rings", Comm. Algebra, 31(2), pp.831~841 (2003)
  4. H. Chen, "On QB1-rings", Comm. Algebra, 34(6), pp.2057~2068 (2006)
  5. H. Chen, "Taiwanese J. Math", 1261–1269, 10(5), pp.1261~1269 (2006)
  6. H. Chen, "Extensions of exchange QB-rings", Algebra Colloq, 13(4), pp.667~674 (2006)
  7. D. Lu, "Comparability, stability, and completions of ideals", Comm. Algebra, 32(7), pp.2617~2634 (2004)
  8. F. Perera, "Lifting units modulo exchange ideals and C¤-algebras with real rank zero", J. Reine Angew. Math, 522, pp.51~62 (2000)
  9. A. A. Tuganbaev, "Rings Close to Regular" (2002), Kluwer Academic Publishers
  10. J. Wei, "Unit-regularity and stable range conditions", Comm. Algebra, 33(6), pp.1937~1946 (2005)

관련 논문AI추천

ON QUASI-STABLE EXCHANGE IDEALSHuanyin Chen대한수학회 · 대한수학회지2010 · 제47권 제1호Rings with many regular elementsEbrahim Nasibi, Nahid Ashrafi대한수학회 · 대한수학회논문집2017 · 제32권 제2호Some Results of QF RingsDong Jun경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제3호Refinement rings, exchange property and comparabilityChaoling Huang대한수학회 · 대한수학회보2011 · 제48권 제3호Quasipolar matrix rings over local ringsJian Cui, Xiaobin Yin대한수학회 · 대한수학회보2014 · 제51권 제3호UNIT-REGULARITY AND STABLE RANGE ONEHuanyin Chen대한수학회 · 대한수학회보2010 · 제47권 제3호

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