On Commutativity of Semiprime Right Goldie C_{k}-Rings

ABSTRACT

This short exposition is about some commutativity conditions on a semiprime right Goldie C_{k}-ring. In particular, it is observed here that a semiprime right Goldie C_{k}-ring with symmetric quotient is commutative. The statement holds if the symmetric ring is replaced by reduced, 2-primal, left duo, right duo, abelian, NI, NCI, IFP, or Armendariz ring.

This short exposition is about some commutativity conditions on a semiprime right Goldie C

Cite this paper

N. Muthana and S. Nauman, "On Commutativity of Semiprime Right Goldie C_{k}-Rings," *Advances in Pure Mathematics*, Vol. 2 No. 4, 2012, pp. 217-219. doi: 10.4236/apm.2012.24031.

N. Muthana and S. Nauman, "On Commutativity of Semiprime Right Goldie C

References

[1] L. Chuang and J. S. Lin, “On Conjecture of Herstein,” Journal of Algebra, Vol. 126, No. 1, 1989, pp. 119-138. doi:10.1016/0021-8693(89)90322-0

[2] A. Klein, I. Nada and H. E. Bell, “Some Commutativity Results for Rings,” Bulletin of the Australian Mathematical Society, Vol. 22, No. 2, 1980, pp. 285-289. doi:10.1017/S0004972700006584

[3] J. Lambek, “On the Representation of Modules by Sheaves of Factor Modules,” Canadian Mathematical Bulletin, Vol. 14, 1971, pp. 359-368. doi:10.4153/CMB-1971-065-1

[4] J. C. McConnell and R. Robson, “Noncommutative Noetherian Rings,” AMS, 2001.

[5] K. R. Goodearl, “Von Neumann Regular Rings,” Monographs and Studies in Math. 4 Pitman, 1979.

[6] G. Marks, “On 2-Primal Ore Extensions,” Communications in Algebra, Vol. 29, No. 5, 2001, pp. 2113-2123. doi:10.1081/AGB-100002173

[7] S. U. Hwang, Y. C. Jeon and K. G. Park, “On NCI Rings,” Bulletin of the Korean Mathematical Society, Vol. 44, No. 2, 2007, pp. 215-223. doi:10.4134/BKMS.2007.44.2.215

[8] G. F. Birkenmeier, H. E. Heatherly and E. K. Lee, “Completely Prime Ideals and Associated Radicals, Ring Theory (Granville, OH 1992),” World Sci. Publ. River H, Edge, 1993, pp. 102-129.

[9] H. E. Bell, “Near-Rings, in Which Every Element Is a Power of Itself,” Bulletin of the Australian Mathematical Society, Vol. 2, No. 3, 1970, pp. 363-368. doi:10.1017/S0004972700042052

[10] K. Ham, Y. Jeon, J. Kang, N. Kim, W. Lee, Y. Lee, S. Ryu and H. Yang, “IFP Rings and Near-IFP Rings,” Journal of the Korean Mathematical Society, Vol. 45, No. 3, 2008, pp. 727-740. doi:10.4134/JKMS.2008.45.3.727

[11] H. K. Kim, N. K. Kim, M. S. Jeong, Y. Lee, S. J. Ryu and D. E. Yeo, “On Conditions Provided by Nil Radicals,” Journal of the Korean Mathematical Society, Vol. 46, 2009, pp. 1027-1040.

[12] M. B. Rege and S. Chhawchharia, “Armendariz Rings,” Proceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 73, No. 1, 1997, pp. 14-17.

[13] T.-K. Lee and T.-L. Wong, “On Armendariz Rings,” Houston Journal of Mathematics, Vol. 29, No. 3, 2003, pp. 583-593.

[14] Y. C. Jeon, H. K. Kim, Y. Lee and J. S. Yoon, “On Weak Armendariz Rings,” Bulletin of the Mathematical Society, Vol. 46, 2009, pp. 135-136.

[15] G. Marks, “A Taxonomy of 2-Primal Rings,” Journal of Algebra, Vol. 266, No. 2, 2003, pp. 494-520. doi:10.1016/S0021-8693(03)00301-6

[1] L. Chuang and J. S. Lin, “On Conjecture of Herstein,” Journal of Algebra, Vol. 126, No. 1, 1989, pp. 119-138. doi:10.1016/0021-8693(89)90322-0

[2] A. Klein, I. Nada and H. E. Bell, “Some Commutativity Results for Rings,” Bulletin of the Australian Mathematical Society, Vol. 22, No. 2, 1980, pp. 285-289. doi:10.1017/S0004972700006584

[3] J. Lambek, “On the Representation of Modules by Sheaves of Factor Modules,” Canadian Mathematical Bulletin, Vol. 14, 1971, pp. 359-368. doi:10.4153/CMB-1971-065-1

[4] J. C. McConnell and R. Robson, “Noncommutative Noetherian Rings,” AMS, 2001.

[5] K. R. Goodearl, “Von Neumann Regular Rings,” Monographs and Studies in Math. 4 Pitman, 1979.

[6] G. Marks, “On 2-Primal Ore Extensions,” Communications in Algebra, Vol. 29, No. 5, 2001, pp. 2113-2123. doi:10.1081/AGB-100002173

[7] S. U. Hwang, Y. C. Jeon and K. G. Park, “On NCI Rings,” Bulletin of the Korean Mathematical Society, Vol. 44, No. 2, 2007, pp. 215-223. doi:10.4134/BKMS.2007.44.2.215

[8] G. F. Birkenmeier, H. E. Heatherly and E. K. Lee, “Completely Prime Ideals and Associated Radicals, Ring Theory (Granville, OH 1992),” World Sci. Publ. River H, Edge, 1993, pp. 102-129.

[9] H. E. Bell, “Near-Rings, in Which Every Element Is a Power of Itself,” Bulletin of the Australian Mathematical Society, Vol. 2, No. 3, 1970, pp. 363-368. doi:10.1017/S0004972700042052

[10] K. Ham, Y. Jeon, J. Kang, N. Kim, W. Lee, Y. Lee, S. Ryu and H. Yang, “IFP Rings and Near-IFP Rings,” Journal of the Korean Mathematical Society, Vol. 45, No. 3, 2008, pp. 727-740. doi:10.4134/JKMS.2008.45.3.727

[11] H. K. Kim, N. K. Kim, M. S. Jeong, Y. Lee, S. J. Ryu and D. E. Yeo, “On Conditions Provided by Nil Radicals,” Journal of the Korean Mathematical Society, Vol. 46, 2009, pp. 1027-1040.

[12] M. B. Rege and S. Chhawchharia, “Armendariz Rings,” Proceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 73, No. 1, 1997, pp. 14-17.

[13] T.-K. Lee and T.-L. Wong, “On Armendariz Rings,” Houston Journal of Mathematics, Vol. 29, No. 3, 2003, pp. 583-593.

[14] Y. C. Jeon, H. K. Kim, Y. Lee and J. S. Yoon, “On Weak Armendariz Rings,” Bulletin of the Mathematical Society, Vol. 46, 2009, pp. 135-136.

[15] G. Marks, “A Taxonomy of 2-Primal Rings,” Journal of Algebra, Vol. 266, No. 2, 2003, pp. 494-520. doi:10.1016/S0021-8693(03)00301-6