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ABELIAN GROUPS WITH LEFT COMORPHIC ENDOMORPHISM RINGS

Yıl 2021, Cilt: 30 Sayı: 30, 217 - 230, 17.07.2021
https://doi.org/10.24330/ieja.969907

Öz

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.

Kaynakça

  • 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.
Yıl 2021, Cilt: 30 Sayı: 30, 217 - 230, 17.07.2021
https://doi.org/10.24330/ieja.969907

Öz

Kaynakça

  • 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.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Grigore Calugareanu Bu kişi benim

Andrey Chekhlov Bu kişi benim

Yayımlanma Tarihi 17 Temmuz 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 30 Sayı: 30

Kaynak Göster

APA Calugareanu, G., & Chekhlov, A. (2021). ABELIAN GROUPS WITH LEFT COMORPHIC ENDOMORPHISM RINGS. International Electronic Journal of Algebra, 30(30), 217-230. https://doi.org/10.24330/ieja.969907
AMA Calugareanu G, Chekhlov A. ABELIAN GROUPS WITH LEFT COMORPHIC ENDOMORPHISM RINGS. IEJA. Temmuz 2021;30(30):217-230. doi:10.24330/ieja.969907
Chicago Calugareanu, Grigore, ve Andrey Chekhlov. “ABELIAN GROUPS WITH LEFT COMORPHIC ENDOMORPHISM RINGS”. International Electronic Journal of Algebra 30, sy. 30 (Temmuz 2021): 217-30. https://doi.org/10.24330/ieja.969907.
EndNote Calugareanu G, Chekhlov A (01 Temmuz 2021) ABELIAN GROUPS WITH LEFT COMORPHIC ENDOMORPHISM RINGS. International Electronic Journal of Algebra 30 30 217–230.
IEEE G. Calugareanu ve A. Chekhlov, “ABELIAN GROUPS WITH LEFT COMORPHIC ENDOMORPHISM RINGS”, IEJA, c. 30, sy. 30, ss. 217–230, 2021, doi: 10.24330/ieja.969907.
ISNAD Calugareanu, Grigore - Chekhlov, Andrey. “ABELIAN GROUPS WITH LEFT COMORPHIC ENDOMORPHISM RINGS”. International Electronic Journal of Algebra 30/30 (Temmuz 2021), 217-230. https://doi.org/10.24330/ieja.969907.
JAMA Calugareanu G, Chekhlov A. ABELIAN GROUPS WITH LEFT COMORPHIC ENDOMORPHISM RINGS. IEJA. 2021;30:217–230.
MLA Calugareanu, Grigore ve Andrey Chekhlov. “ABELIAN GROUPS WITH LEFT COMORPHIC ENDOMORPHISM RINGS”. International Electronic Journal of Algebra, c. 30, sy. 30, 2021, ss. 217-30, doi:10.24330/ieja.969907.
Vancouver Calugareanu G, Chekhlov A. ABELIAN GROUPS WITH LEFT COMORPHIC ENDOMORPHISM RINGS. IEJA. 2021;30(30):217-30.