Table of Contents
Algebra
Volume 2015, Article ID 183930, 6 pages
http://dx.doi.org/10.1155/2015/183930
Research Article

On -Absorbing Primary Elements in Lattice Modules

Department of Mathematics, Savitribai Phule Pune University, Pune 411 007, India

Received 18 December 2014; Accepted 31 March 2015

Academic Editor: Andrei V. Kelarev

Copyright © 2015 Sachin Ballal and Vilas Kharat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. F. Çallıalp, C. Jayaram, and Ü. Tekir, “Weakly prime elements in multiplicative lattices,” Communications in Algebra, vol. 40, no. 8, pp. 2825–2840, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. S. B. Ballal, M. T. Gophane, and V. S. Kharat, “On weakly primary elements in multiplicative lattices,” Southeast Asian Bulletin of Mathematics. In press.
  3. C. Jayaram, Ü. Tekir, and E. Yetkin, “2-absorbing and weakly 2-absorbing elements in multiplicative lattices,” Communications in Algebra, vol. 42, no. 6, pp. 2338–2353, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. V. V. Joshi and S. B. Ballal, “A note on n-Baer multiplicative lattices,” Southeast Asian Bulletin of Mathematics, vol. 39, pp. 67–76, 2015. View at Google Scholar
  5. S. B. Ballal and V. S. Kharat, “On generalization of prime, weakly prime and almost prime elements in multiplicative lattices,” International Journal of Algebra, vol. 8, no. 9, pp. 439–449, 2014. View at Publisher · View at Google Scholar
  6. C. S. Manjarekar and A. V. Bingi, “-prime and -primary elements in multiplicative lattices,” Algebra, vol. 2014, Article ID 890312, 7 pages, 2014. View at Publisher · View at Google Scholar
  7. A. Badawi, Ü. Tekir, and E. Yetkin, “On 2-absorbing primary ideals in commutative rings,” Bulletin of the Korean Mathematical Society, vol. 51, no. 4, pp. 1163–1173, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  8. E. A. Al-Khouja, “Maximal elements and prime elements in lattice modules,” Damascus University for Basic Sciences, vol. 19, pp. 9–20, 2003. View at Google Scholar
  9. F. Callialp and Ü. Tekir, “Multiplication lattice modules,” Iranian Journal of Science and Technology, vol. 35, no. 4, pp. 309–313, 2011. View at Google Scholar · View at MathSciNet
  10. E. W. Johnson and J. A. Johnson, “Lattice modules over principal element domains,” Communications in Algebra, vol. 31, no. 7, pp. 3505–3518, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. H. M. Nakkar and D. D. Anderson, “Associated and weakly associated prime elements and primary decomposition in lattice modules,” Algebra Universalis, vol. 25, no. 2, pp. 196–209, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. F. Alarcon, D. D. Anderson, and C. Jayaram, “Some results on abstract commutative ideal theory,” Periodica Mathematica Hungarica, vol. 30, no. 1, pp. 1–26, 1995. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. D. D. Anderson, “Abstract commutative ideal theory without chain condition,” Algebra Universalis, vol. 6, no. 2, pp. 131–145, 1976. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. R. P. Dilworth, “Abstract commutative ideal theory,” Pacific Journal of Mathematics, vol. 12, pp. 481–498, 1962. View at Publisher · View at Google Scholar · View at MathSciNet