DOI QR코드

DOI QR Code

Examples of Central Semicommutative Rings

  • Wang, Yingying (School of Mathematics and Information Science, Shandong Institute of Business and Technology)
  • Received : 2017.09.09
  • Accepted : 2018.08.06
  • Published : 2018.09.23

Abstract

An example of a strongly central semicommutative ring which is not semicommutative is constructed. This answers a question of Bhattachafjee and Chakraborty negatively.

Keywords

central reduced rings;central semicommutative rings;strongly central semicommutative rings

Acknowledgement

Supported by : NSF of Shandong Province

References

  1. D. D. Anderson, V. Camillo, Semigroups and rings whose zero products commute, Comm. Algebra, 27(1999), 2847-2852. https://doi.org/10.1080/00927879908826596
  2. A. Bhattacharjee and U. S. Chakraborty, On some generalizations of reversible and semicommutative rings, Int. Electron. J. Algebra, 22(2017), 11-27.
  3. P. M. Cohn, Reversible rings, Bull. London Math. Soc., 31(1999), 641-648. https://doi.org/10.1112/S0024609399006116
  4. C. Huh, H. K. Kim, N. K. Kim and Y. Lee, Basic examples and extensions of symmetric rings, J. Pure Appl. Algebra, 202(2005), 154-167. https://doi.org/10.1016/j.jpaa.2005.01.009
  5. D. W. Jung, N. K. Kim, Y. Lee and S. J. Ryu, On properties related to reversible rings, Bull. Korean Math. Soc., 52(2015), 247-261. https://doi.org/10.4134/BKMS.2015.52.1.247
  6. G. Kafkas, B. Ungor, S. Halicioglu and A. Harmanci, Generalized symmetric rings, Algebra Discrete Math., 12(2011), 72-84.
  7. H. Kose, B. Ungor, S. Halicioglu and A. Harmanci, A generalization of reversible rings, Iran. J. Sci. Technol. Trans. A Sci., 38(1)(2014), 43-48.
  8. J. Krempa, Some examples of reduced rings, Algebra Colloq., 3(1996), 289-300.
  9. J. Lambek, On the representation of modules by sheaves of factor modules, Canad. Math. Bull., 14(1971), 359-368. https://doi.org/10.4153/CMB-1971-065-1
  10. G. Marks, Reversible rings and symmetric rings, J. Pure Appl. Algebra, 174(2002), 311-318. https://doi.org/10.1016/S0022-4049(02)00070-1
  11. G. Marks, A taxonomy of 2-primal rings, J. Algebra, 266(2003), 494-520. https://doi.org/10.1016/S0021-8693(03)00301-6
  12. L. Motais de Narbonne, Anneaux semi-commutatifs et uniseriels; anneaux dont les ideaux principaux sont idempotents, Proceedings of the 106th National Congress of Learned Societies (Perpignan, 1981), Bib. Nat., Paris, 1982, 71-73.
  13. T. Ozen, N. Agayev and A. Harmanci, On a class of semicommutative rings, Kyungpook Math. J., 51(2011), 283-291.
  14. B. Ungor, S. Halicioglu, H. Kose and A. Harmanci, Rings in which every nilpotent is central, Algebra Groups Geom., 30(2013), 1-18.
  15. G. Yang and R. Du, Rings over which polynomial rings are semi-commutative, Vietnam J. Math., 37(2009), 527-535.