•  
  •  
 

Al-Bahir Journal for Engineering and Pure Sciences

Abstract

Let R be a ring and M be a right R-module. A submodule of is said to be g-small in , if for every submodule , with implies that . Then is a g-small submodule of . We call g-coatomic module whenever and then . Also, is called right (left) g-coatomic ring if the right (left) -module (R) is g-coatomic. In this work, we study g-coatomic modules and ring. We investigate some properties of these modules. We prove is g-coatomic if and only if each is g-coatomic. It is proved that if is a g-semiperfect ring with , then is g-coatomic ring.

References

  1. Anderson FW, Fuller KR. Rings and categories of modules. New York: Springer-Verlag; 1974.
  2. Goodearl KR. Ring Theory: nonsingular rings and modules. New York: Dekker; 1976.
  3. Gungoroglu G. Coatomic modules. Far East J Math Sci 1998:153-62. Special Volume, Part II. https://www.emis.de/journals/FEJMS/vol/special2.pdf
  4. Kasch F. Modules and rings. Academic Press; 1982.
  5. Kosan MT, Harmanci A. Generalizations of coatomic modules. Cent Eur J Math 2005;3(2):273-81. https://link.springer.com/article/10.2478/BF02475911
  6. Kos¸ar B, Nebiyev C, Pekin A. A generalization of g-supplemented modules. Miskolc Math Notes 2019;20(1):345-52. https://doi.org/10.18514/MMN.2019.2327
  7. Lomp C. On semilocal modules and rings. Commun Algebra 1999;27(4):1921-35. https://doi.org/10.1080/00927879908826552
  8. Nebiyev C, Ӧkten HH. Weakly g-supplemented modules. Eur J Pure Appl Math 2017;10(3):521-8. http://www.ejpam.com/index.php/ejpam/article/view/294
  9. Wisbauer R. Foundations of module and ring theory. Reading: Gordon & Breach; 1991.
  10. Zhou Y. Generalizations of perfect, semiperfect, and semiregular rings. Algebra Colloq 2000;7(3):305-18.
  11. Yousif MY, Zhou Y. Semiregular, semiperfect and perfect rings relative to an ideal. Rocky Mt J Math 2002;32(4):1651-71. https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-32/issue-4/Semiregular-semiperfect-and-perfect-rings-relative-to-an-ideal/rmjmo/1103072608.full
  12. Zhou DX, Zhang XR. Small-essential submodules and morita duality. Southeast Asian Bull Math 2011;35:1051-62.

Download

Included in

Algebra Commons

Share

COinS