DOI QR코드

DOI QR Code

BAER SPECIAL RINGS AND REVERSIBILITY

  • Jin, Hai-Lan (Department of Mathematics Yanbian University)
  • 투고 : 2013.10.29
  • 심사 : 2014.08.05
  • 발행 : 2014.11.15

초록

In this paper, we apply some properties of reversible rings, Baerness of fixed rings, skew group rings and Morita Context rings to get conditions that shows fixed rings, skew group rings and Morita Context rings are reversible. Moreover, we investigate conditions in which Baer rings are reversible and reversible rings are Baer.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China

참고문헌

  1. G. F. Birkenmeier, J. Y. Kim, and J. K. Park, On quasi-Baer rings, Duck Math J. 37 (1970), 127-128.
  2. G. F. Birkenmeier, J. Y. Kim, and J. K. Park, Principally quasi-Baer rings, Comm. Algebra 29 (2001), 1-22. https://doi.org/10.1081/AGB-100000782
  3. G. F. Birkenmeier, J. Y. Kim, and J. K. Park, Semicentral reduced algebra International symposium on ring teory, Bikhauser, Boston (2001), 67-84.
  4. P. M. Cohn, Reversible rings, Bull. London Math. Soc. 31 (1999), 641-648. https://doi.org/10.1112/S0024609399006116
  5. J. M. Habeb, A note on zero commutative and duo rings, Math. J. Okayama University 32 (1990), 73-76.
  6. C. Y. Hong, N. K. Kim, and T. K. Kwak, Ore extensions of Baer and p.p.-rings, Journal of Pure and Applied Algebra 151 (2000), 215-226. https://doi.org/10.1016/S0022-4049(99)00020-1
  7. T. W. Hungerford, Algebra, New York: Springer-Verlag, 1980.
  8. H. L. Jin, Principally Quasi-Baer Skew Group Rings and Fixed Rings: [Sc.D.Dissertation], College of Science Pusan National University:Pusan, 2003.
  9. H. L. Jin and Q. X. Zhao, The (Quasi-)Baerness of Skew Group Ring and Fixed Ring, Sientific Reserch 1 (2011), 363-366.
  10. K. Morita, Duality for modules and its application to the theory of rings with minimum conditions, Science Reports of the Tokyo Kyoiku Daigoku Sect. A. 6 (1958), 83-142.
  11. N. K. Kim and Y. Lee, Extension of reversible rings, Journal of Pure and Applied Algebra. 185 (2003), 207-223. https://doi.org/10.1016/S0022-4049(03)00109-9
  12. J. Lambek, On the representation of modules by sheaves of factor modules, Canad. Math. Bull. 14 (1997), 359-368.
  13. T. Y. Lam, Lectures on modules and rings, New York:Springer-Verlag. 1999.
  14. Q. Liu and B. Y. OuYang, Rickart modules, Journal of Nanjing University. 23 (2006), 157-166.
  15. J. Li, Condition for Morita Context ring become the (quasi-)Baer ring, Yan ji: yanbian University, 2010.
  16. G. Marks, Reversible and symmetric rings, Journal of Pure and Applied Alge-bra 174 (2002), 311-318. https://doi.org/10.1016/S0022-4049(02)00070-1
  17. A. Moussavi and E. Hashemi, On ($\alpha-\delta$)-skew Armendariz rings, J. Korean Math. Soc. 42 (2005), 353-363. https://doi.org/10.4134/JKMS.2005.42.2.353
  18. S. Montgomery, Fixed rings of finite automorphism groups of associative rings, New York:Springer-Verlag, 1980.
  19. Y. Wang and Y. L. Ren, The property of the morita context ring, Journal of jilin University. 44 (2006), 519-526.
  20. Y. H. Wang and Y. L. Ren, The property of the Abel ring, Journal of Linyi normal University. 6 (2009), 14-17.