대한수학회지 (Journal of the Korean Mathematical Society)

  • 제42권6호
  • /
  • Pages.1153-1167
  • /
  • 2005
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

R-HOMOMORPHISMS AND R-HOMOGENEODS MAPS

  • Cho, Yong-Uk (Department of Mathematics Education College of Education Silla University)
  • 발행 : 2005.11.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, all rings and all near-rings R are associative, all modules are right R-modules. For a near-ring R, we consider representations of R as R-groups. We start with a study of AGR rings and their properties. Next, for any right R-module M, we define a new concept GM module and investigate the commutative property of faithful GM modules and some characterizations of GM modules. Similarly, for any near-ring R, we introduce an R-group with MR-property and some properties of MR groups.

키워드

참고문헌

  1. F. W. Anderson and K. R. Fuller, Rings and categories of modules, Springer- Verlag, New York, Heidelberg, Berlin, 1974
  2. P. B. Bhattacharya, S. K. Jain, and S. R. Nagpaul, Basic Abstract Algebra, Cambridge University Press, 1994
  3. G. F. Birkenmeier and Y. U. Cho, Additive endomorphisms generated by ring endomorphisms, East-West J. Math. 1 (1998), no. 1, 73-84
  4. S. Dhompongsa and J. Sanwong, Rings in which additive mappings are multi- plicative, Studia Sci. Math. Hungar. 22 (1987), 357-359
  5. M. Dugas, J. Hausen, and J. A. Johnson, Rings whose additive endomorphisms are multiplicative, Period. Math. Hungar. 23 (1991), 65-73 https://doi.org/10.1007/BF02260395
  6. M. Dugas, J. Hausen, and J. A. Johnson, Rings whose additive endomorphisms are ring endomorphisms, Bull. Austral. Math. Soc. 45 (1992), 91-103 https://doi.org/10.1017/S0004972700037047
  7. S. Feigelstock, Rings whose additive endomorphisms are multiplicative, Period. Math. Hungar. 19 (1988), 257-260 https://doi.org/10.1007/BF01848834
  8. Y. Hirano, On rings whose additive endomorphisms are multiplicative, Period. Math. Hungar. 23 (1991), 87-89 https://doi.org/10.1007/BF02260397
  9. A. V. Kelarev, On left self distributive rings, Acta Math. Hungar. 71 (1996), 121-122 https://doi.org/10.1007/BF00052200
  10. K. H. Kim and F. W. Roush, Additive endomorphisms of rings, Period. Math. Hungar. 12 (1981), 241-242 https://doi.org/10.1007/BF01849611
  11. C. G. Lyons and J. D. P. Meldrum, Characterizing series for faithful D.G. near- rings, Proc. Amer. Math. Soc. 72 (1978), 221-227 https://doi.org/10.2307/2042780
  12. S. J. Mahmood and J. D. P. Meldrum, D.G. near-rings on the infinite dihe- dral groups, Near-rings and Near-fields (1987), Elsevier Science Publishers B.V (North-Holland), 151-166
  13. C. J. Maxson and K. C. Smith, Simple near-ring centralizers of finite rings, Proc. Amer. Math. Soc. 75 (1979), 8-12
  14. C. J. Maxson and K. C. Smith, The centralizer of a group endomorphism, J. Algebra 57 (1979), 441- 448 https://doi.org/10.1016/0021-8693(79)90231-X
  15. C. J. Maxson and A. B. Van der Merwe, Forcing linearity numbers for modules over rings with nontrivial idempotents, J. Algebra 256 (2002), 66-84 https://doi.org/10.1016/S0021-8693(02)00128-X
  16. J. D. P. Meldrum, Near-rings and their links with groups, Pitman, Boston, London and Melbourne, 1985
  17. J. D. P. Meldrum, Upper faithful D.G. near-rings, Proc. Edinb. Math. Soc. 26 (1983), 361-370 https://doi.org/10.1017/S0013091500004430
  18. G. Pilz, Near-rings, North Holland, Amsterdam, New York and Oxford, 1983
  19. R. P. Sullivan, Research problem, Period. Math. Hungar. 8 (1977), no. 23, 313- 314 https://doi.org/10.1007/BF02018414

피인용 문헌

  1. SOME RESULTS ON IFP NEAR-RINGS vol.31, pp.4, 2009, https://doi.org/10.5831/HMJ.2009.31.4.639