대한수학회지 (Journal of the Korean Mathematical Society)

  • 제53권1호
  • /
  • Pages.217-232
  • /
  • 2016
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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ON IDEMPOTENTS IN RELATION WITH REGULARITY

  • HAN, JUNCHEOL (DEPARTMENT OF MATHEMATICS EDUCATION PUSAN NATIONAL UNIVERSITY) ;
  • LEE, YANG (DEPARTMENT OF MATHEMATICS EDUCATION PUSAN NATIONAL UNIVERSITY) ;
  • PARK, SANGWON (DEPARTMENT OF MATHEMATICS DONG-A UNIVERSITY) ;
  • SUNG, HYO JIN (DEPARTMENT OF MATHEMATICS EDUCATION PUSAN NATIONAL UNIVERSITY) ;
  • YUN, SANG JO (DEPARTMENT OF MATHEMATICS EDUCATION PUSAN NATIONAL UNIVERSITY)
  • 투고 : 2014.10.31
  • 발행 : 2016.01.01
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초록

We make a study of two generalizations of regular rings, concentrating our attention on the structure of idempotents. A ring R is said to be right attaching-idempotent if for $a{\in}R$ there exists $0{\neq}b{\in}R$ such that ab is an idempotent. Next R is said to be generalized regular if for $0{\neq}a{\in}R$ there exist nonzero $b{\in}R$ such that ab is a nonzero idempotent. It is first checked that generalized regular is left-right symmetric but right attaching-idempotent is not. The generalized regularity is shown to be a Morita invariant property. More structural properties of these two concepts are also investigated.

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과제정보

연구 과제 주관 기관 : Pusan National University

참고문헌

  1. A. Badawi, On semicommutative $\pi$-regular rings, Comm. Algebra 22 (1994), no. 1, 151-157. https://doi.org/10.1080/00927879408824837
  2. J. L. Dorroh, Concerning adjunctions to algebras, Bull. Amer. Math. Soc. 38 (1932), no. 2, 85-88. https://doi.org/10.1090/S0002-9904-1932-05333-2
  3. K. R. Goodearl, Von Neumann Regular Rings, Pitman, London, 1979.
  4. M. Henriksen, On a class of regular rings that are elementary divisor ring, Arch. Math. 24 (1973), 133-141. https://doi.org/10.1007/BF01228189
  5. C. Huh, N. K. Kim, and Y. Lee, Examples of strongly $\pi$-regular rings, J. Pure Appl. Algebra 189 (2004), no. 1-3, 195-210. https://doi.org/10.1016/j.jpaa.2003.10.032
  6. C. Huh, Y. Lee, and A. Somktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra 30 (2002), no. 2, 751-761. https://doi.org/10.1081/AGB-120013179
  7. N. Jacobson, Some remarks on one-sided inverses, Proc. Amer. Math. Soc. 1 (1950), 352-355.
  8. J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, John Wiley & Sons Ltd., Chichester, New York, Brisbane, Toronto, Singapore, 1987.
  9. W. K. Nicholson, I- rings, Trans. Amer. Math. Soc. 207 (1975), 361-373.
  10. G. Y. Shin, Prime ideals and sheaf representation of a pseudo symmetric ring, Trans. Amer. Math. Soc. 184 (1973), 43-60. https://doi.org/10.1090/S0002-9947-1973-0338058-9