ABELIAN GROUPS WITH LEFT COMORPHIC ENDOMORPHISM RINGS

A ring $R$ is called left comorphic if for every $a\in R$ there exists $b\in R$ such that the left and right annihilators satisfy $Ra=l(b)$ and $r(a)=bR$. In this paper, the Abelian groups with left comorphic endomorphism rings are completely determined.

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  • M. Alkan, W. K. Nicholson, and A. C . Ozcan, Comorphic rings, J. Algebra Appl., 17(4) (2018), 1850075 (21 pp).
  • G. Calugareanu, Morphic abelian groups, J. Algebra Appl., 9(2) (2010), 185-193.
  • G. Calugareanu, Abelian groups with left morphic endomorphism ring, J. Algebra Appl., 17(9) (2018), 1850176 (8 pp).
  • G. Calugareanu and L. Pop, Morphic objects in categories, Bull. Math. Soc. Sci. Math. Roumanie, 56(104)(2) (2013), 173-180.
  • A. R. Chekhlov, Abelian groups with annihilator ideals of endomorphism rings, Sib. Math. J., 59(2) (2018), 363-367.
  • S. Dascalescu, C. Nastasescu, A. Tudorache and L. Daus, Relative regular objects in categories, Appl. Categ. Structures, 14(5-6) (2006), 567-577.
  • L. Fuchs, Infinite Abelian Groups. Vol. I., Academic Press, New York-London, 1970.
  • L. Fuchs, Infinite Abelian Groups. Vol. II., Academic Press, New York-London, 1973.
  • S. Glaz and W. Wickless, Regular and principal projective endomorphism rings of mixed abelian groups, Comm. Algebra, 22(4) (1994), 1161-1176.
  • A.V. Ivanov, Abelian groups with self-injective endomorphism rings and endomorphism rings with annihilator condition, In: Abelian Groups and Modules [Russian], Tomsk. Gos. Univ., Tomsk, (1982), 93-109.
  • M.A. Kil'p, Quasi-injective abelian groups [Russian], Vestnik Moskov. Univ. Ser. I Mat. Meh., 22(3) (1967), 3-4.
  • G. Lee, S. T. Rizvi and C. S. Roman, Rickart modules, Comm. Algebra, 38(11) (2010), 4005-4027.
  • W. K. Nicholson and E. Sanchez Campos, Rings with the dual of the isomorphism theorem, J. Algebra, 271(1) (2004), 391-406.
  • W. K. Nicholson, A survey of morphic modules and rings, Advances in Ring Theory (Nanjing 2004), World Sci. Publ., Hackensack, NJ, (2005), 167-180.
  • W. K. Nicholson and M. F. Yousif, Principally injective rings, J. Algebra, 174 (1995), 77-93.
  • [16] K. M. Rangaswamy, Abelian groups with self-injective endomorphism rings, Lect. Notes. Math., 372 (1974), 595-604.
  • S. T. Rizvi and C. S. Roman, Baer and quasi-Baer modules, Comm. Algebra, 32(1) (2004), 103-123.
  • J. Zelmanowitz, Regular modules, Trans. Amer. Math. Soc., 163 (1972), 341-355.
  • H. Zhu and N. Ding, Generalized morphic rings and their applications, Comm. Algebra, 35(9) (2007), 2820-2837.