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Rings close to semiregular

이양|A. Cigdem Ozcan|Pinar Aydogdu
대한수학회 (The Korean Mathematical Society)|2012.05|대한수학회지 (Journal of the KMS)|제49권 제3호|pp. 605-622|DOI http://dx.doi.org/

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키워드

idempotent liftingsemi unit-regular ringsemi (strongly) π-regular ring.
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초록

A ring R is called semiregular if R/J is regular and idem-potents lift modulo J, where J denotes the Jacobson radical of R. We give some characterizations of rings R such that idempotents lift modulo J, and R=J satis es one of the following conditions: (one-sided) unit-regular, strongly regular, (unit, strongly, weakly) π-regular.

Abstract

A ring R is called semiregular if R/J is regular and idem-potents lift modulo J, where J denotes the Jacobson radical of R. We give some characterizations of rings R such that idempotents lift modulo J, and R=J satis es one of the following conditions: (one-sided) unit-regular, strongly regular, (unit, strongly, weakly) π-regular.

참고문헌 (30)

  1. P. Ara, "Strongly {regular rings have stable range one", Proc. Amer. Math. Soc, 124(11), pp.3293~3298 (1996)
  2. R. F. Arens, "Topological representations of algebras", Trans. Amer. Math. Soc, 63, pp.457~481 (1948)
  3. G. Azumaya, "Strongly", J. Fac. Sci. Hokkaido Univ. Ser. I, 13, pp.34~39 (1954)
  4. V. P. Camillo, "Stable range one for rings with many idempotents", Trans. Amer. Math. Soc, 347(8), pp.3141~3147 (1995)
  5. V. P. Camillo, "Exchange rings, units and idempotents", Comm. Algebra, 22(12), pp.4737~4749 (1994)
  6. H. Chen, "A note on the regularity of rings", Chinese Quart. J. Math, 13(2), pp.67~71 (1998)
  7. H. Chen, "Exchange rings satisfying unit 1-stable range", Kyushu J. Math, 54, pp.1~6 (2000)
  8. H. Chen, "On strongly stable rings", Comm. Algebra, 31(6), pp.2771~2789 (2003)
  9. H. Chen, "On semiregular rings", New Zealand J. Math, 32, pp.11~20 (2003)
  10. A. Y. M. Chin, "A note on strongly regular rings", Acta Math. Hungar, 102(4), pp.337~342 (2004)
  11. P. Crawley, "Refinements for infinite direct decompositions of algebraic systems", Pacific J. Math, 14, pp.797~855 (1964)
  12. K. R. Goodearl, "Von-Neumann Regular Rings" (1979), Pitman Publishing Limited
  13. V. Gupta, "Weakly regular rings and group rings", Math. J. Okayama Univ, 19(2), pp.123~127 (1977)
  14. Y. Hirano, "Some studies on strongly regular rings", Math. J. Okayama Univ, 20(2), pp.141~149 (1978)
  15. C. H. Hong, "On weak regularity of rings whose prime ideals are maximal", J. Pure Appl. Algebra, 46(1), pp.35~44 (2000)
  16. Qinghe Huang, "-Morphic Rings", Kyungpook Mathematical Journal, 47(3), pp.363~372 (2007), 경북대학교 자연과학대학 수학과
  17. S. U. Hwang, "Structure and topological conditions of NI-rings", J. Algebra, 302(1), pp.186~199 (2006)
  18. Q. Li, "Weak cancellation of modules and weakly stable range conditions for exchange rings", Acta Math. Sinica, 45(6), pp.1121~1126 (2002)
  19. W. K. Nicholson, "Strongly clean rings and fitting's lemma", Comm. Algebra, 27(8), pp.3583~3592 (1999)
  20. W. K. Nicholson, "Quasi Frobenius Rings, Cambridge Tracts in Math" (2003), Cambridge University Press
  21. W. K. Nicholson, "Strong lifting", J. Algebra, 285(2), pp.795~818 (2005)
  22. V. S. Ramamurthi, "Weakly regular rings", Canad. Math. Bull, 16, pp.317~321 (1973)
  23. A. A. Tuganbaev, "Semiregular, weakly regular and {regular rings", J. Math. Sci. (New York), 109(3), pp.1509~1588 (2002)
  24. L. N. Vaserstein, "Bass's first stable range condition", J. Pure Appl. Algebra, 34(2), pp.319~330 (1984)
  25. R. B. Warfield, "Exchange rings and decomposition of modules", Math. Ann, 199, pp.31~36 (1972)
  26. T. S. Wu, "Weak cancellation of modules and the weak stable range one condition", Nanjing Daxue Xuebao Shuxue Bannian Kan, 11(2), pp.109~116 (1994)
  27. T. S. Wu, "Inner weak cancellation of modules", Nanjing Daxue Xuebao Shuxue Bannian Kan, 13(1), pp.54~57 (1996)
  28. G. Xiao, "Generalizations of semiregular rings", Comm. Algebra, 33(10), pp.3447~3465 (2005)
  29. H. P. Yu, "On quasiduo rings", Glasg. Math. J, 37(1), pp.21~31 (1995)
  30. H. P. Yu, "On the structure of exchange rings", Comm. Algebra, 25(2), pp.661~670 (1997)

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