BibTex RIS Kaynak Göster

STABLE TORSION THEORIES AND THE INJECTIVE HULLS OF SIMPLE MODULES

Yıl 2014, , 89 - 98, 01.12.2014

Can Hatipoğlu

https://doi.org/10.24330/ieja.266229
Cited By: 1

Öz

A torsion theoretical characterization of left Noetherian rings over
which injective hulls of simple left modules are locally Artinian is given. Suf-
ficient conditions for a left Noetherian ring to satisfy this finiteness condition
are obtained in terms of torsion theories.

Anahtar Kelimeler

Injective modules simple modules stable torsion theories

Kaynakça

  • P. A. A. B. Carvalho, C. Hatipoglu and C. Lomp, Injective hulls of simple modules over differential operator rings, arXiv:1211.2592.
  • P. A. A. B. Carvalho, C. Lomp and D. Pusat-Yilmaz, Injective modules over down-up algebras, Glasg. Math. J., 52(A) (2010), 53-59.
  • P. A. A. B. Carvalho and I. M. Musson, Monolithic modules over Noetherian rings, Glasg. Math. J., 53(3) (2011), 683-692.
  • J. Clark, C. Lomp, N. Vanaja and R. Wisbauer, Lifting Modules, Supplements and projectivity in module theory. Frontiers in Mathematics. Birkh¨auser Ver- lag, Basel, 2006.
  • S. E. Dickson, A torsion theory for Abelian categories, Trans. Amer. Math. Soc., 121 (1966), 223-235.
  • N. V. Dung, D. V. Huynh, P. F. Smith and R. Wisbauer, Extending Modules, With the collaboration of John Clark and N. Vanaja. Pitman Research Notes in Mathematics Series, 313. Longman Scientific & Technical, Harlow, 1994.
  • C. Faith, On hereditary rings and Boyle’s conjecture, Arch. Math. (Basel), (2) (1976), 113-119.
  • J. S. Golan, Torsion Theories, Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1986.
  • A. W. Goldie, Torsion-free modules and rings, J. Algebra, 1 (1964), 268-287.
  • C. Hatipo˘glu and C. Lomp, Injective hulls of simple modules over finite di- mensional nilpotent complex Lie superalgebras, J. Algebra, 361 (2012), 79-91.
  • A. V. Jategaonkar, Jacobson’s conjecture and modules over fully bounded Noe- therian rings, J. Algebra, 30 (1974), 103-121.
  • T. Y. Lam, Lectures on modules and rings, Graduate Texts in Mathematics, Springer-Verlag, New York, 1999.
  • J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, With the cooperation of L. W. Small. Graduate Studies in Mathematics, 30. Amer. Math. Soc., Providence, RI, 2001.
  • I. M. Musson, Injective modules for group rings of polycyclic groups I, II, Quart. J. Math. Oxford Ser. (2), 31(124) (1980), 429-448, 449-466.
  • I. M. Musson, Some examples of modules over Noetherian rings, Glasgow Math. J., 23(1) (1982), 9-13.
  • I. M. Musson, Finitely generated, non-artinian monolithic modules, Contemp. Math., 562, Amer. Math. Soc., Providence, RI, 2012.
  • G. Renault, Etude des sous-modules compl´ements dans un module, Bull. Soc. Math. France M´em., 9 (1967), 79 pp.
  • P. F. Smith, Injective modules and prime ideals, Comm. Algebra, 9(9) (1981), 999.
  • B. Stenstr¨om, Rings of Quotients, An introduction to methods of ring theory. Springer-Verlag, New York-Heidelberg, 1975.
  • M. L. Teply, Some aspects of Goldie’s torsion theory, Pacific J. Math., 29 (1969), 447-459.
  • M. L. Teply, Torsionfree projective modules, Proc. Amer. Math. Soc., 27 (1971), 34. Can Hatipo˘glu
  • Center of Mathematics University of Porto Rua do Campo Alegre 687 007, Porto, Portugal e-mail: chatipoglu@alunos.fc.up.pt

Yıl 2014, , 89 - 98, 01.12.2014

Can Hatipoğlu

https://doi.org/10.24330/ieja.266229
Cited By: 1

Öz

Kaynakça

  • P. A. A. B. Carvalho, C. Hatipoglu and C. Lomp, Injective hulls of simple modules over differential operator rings, arXiv:1211.2592.
  • P. A. A. B. Carvalho, C. Lomp and D. Pusat-Yilmaz, Injective modules over down-up algebras, Glasg. Math. J., 52(A) (2010), 53-59.
  • P. A. A. B. Carvalho and I. M. Musson, Monolithic modules over Noetherian rings, Glasg. Math. J., 53(3) (2011), 683-692.
  • J. Clark, C. Lomp, N. Vanaja and R. Wisbauer, Lifting Modules, Supplements and projectivity in module theory. Frontiers in Mathematics. Birkh¨auser Ver- lag, Basel, 2006.
  • S. E. Dickson, A torsion theory for Abelian categories, Trans. Amer. Math. Soc., 121 (1966), 223-235.
  • N. V. Dung, D. V. Huynh, P. F. Smith and R. Wisbauer, Extending Modules, With the collaboration of John Clark and N. Vanaja. Pitman Research Notes in Mathematics Series, 313. Longman Scientific & Technical, Harlow, 1994.
  • C. Faith, On hereditary rings and Boyle’s conjecture, Arch. Math. (Basel), (2) (1976), 113-119.
  • J. S. Golan, Torsion Theories, Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1986.
  • A. W. Goldie, Torsion-free modules and rings, J. Algebra, 1 (1964), 268-287.
  • C. Hatipo˘glu and C. Lomp, Injective hulls of simple modules over finite di- mensional nilpotent complex Lie superalgebras, J. Algebra, 361 (2012), 79-91.
  • A. V. Jategaonkar, Jacobson’s conjecture and modules over fully bounded Noe- therian rings, J. Algebra, 30 (1974), 103-121.
  • T. Y. Lam, Lectures on modules and rings, Graduate Texts in Mathematics, Springer-Verlag, New York, 1999.
  • J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, With the cooperation of L. W. Small. Graduate Studies in Mathematics, 30. Amer. Math. Soc., Providence, RI, 2001.
  • I. M. Musson, Injective modules for group rings of polycyclic groups I, II, Quart. J. Math. Oxford Ser. (2), 31(124) (1980), 429-448, 449-466.
  • I. M. Musson, Some examples of modules over Noetherian rings, Glasgow Math. J., 23(1) (1982), 9-13.
  • I. M. Musson, Finitely generated, non-artinian monolithic modules, Contemp. Math., 562, Amer. Math. Soc., Providence, RI, 2012.
  • G. Renault, Etude des sous-modules compl´ements dans un module, Bull. Soc. Math. France M´em., 9 (1967), 79 pp.
  • P. F. Smith, Injective modules and prime ideals, Comm. Algebra, 9(9) (1981), 999.
  • B. Stenstr¨om, Rings of Quotients, An introduction to methods of ring theory. Springer-Verlag, New York-Heidelberg, 1975.
  • M. L. Teply, Some aspects of Goldie’s torsion theory, Pacific J. Math., 29 (1969), 447-459.
  • M. L. Teply, Torsionfree projective modules, Proc. Amer. Math. Soc., 27 (1971), 34. Can Hatipo˘glu
  • Center of Mathematics University of Porto Rua do Campo Alegre 687 007, Porto, Portugal e-mail: chatipoglu@alunos.fc.up.pt
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Diğer ID JA42TE59CP
Bölüm Makaleler
Yazarlar

Can Hatipoğlu Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2014
Yayımlandığı Sayı Yıl 2014

Kaynak Göster

APA Hatipoğlu, C. (2014). STABLE TORSION THEORIES AND THE INJECTIVE HULLS OF SIMPLE MODULES. International Electronic Journal of Algebra, 16(16), 89-98. https://doi.org/10.24330/ieja.266229
AMA Hatipoğlu C. STABLE TORSION THEORIES AND THE INJECTIVE HULLS OF SIMPLE MODULES. IEJA. Aralık 2014;16(16):89-98. doi:10.24330/ieja.266229
Chicago Hatipoğlu, Can. “STABLE TORSION THEORIES AND THE INJECTIVE HULLS OF SIMPLE MODULES”. International Electronic Journal of Algebra 16, sy. 16 (Aralık 2014): 89-98. https://doi.org/10.24330/ieja.266229.
EndNote Hatipoğlu C (01 Aralık 2014) STABLE TORSION THEORIES AND THE INJECTIVE HULLS OF SIMPLE MODULES. International Electronic Journal of Algebra 16 16 89–98.
IEEE C. Hatipoğlu, “STABLE TORSION THEORIES AND THE INJECTIVE HULLS OF SIMPLE MODULES”, IEJA, c. 16, sy. 16, ss. 89–98, 2014, doi: 10.24330/ieja.266229.
ISNAD Hatipoğlu, Can. “STABLE TORSION THEORIES AND THE INJECTIVE HULLS OF SIMPLE MODULES”. International Electronic Journal of Algebra 16/16 (Aralık 2014), 89-98. https://doi.org/10.24330/ieja.266229.
JAMA Hatipoğlu C. STABLE TORSION THEORIES AND THE INJECTIVE HULLS OF SIMPLE MODULES. IEJA. 2014;16:89–98.
MLA Hatipoğlu, Can. “STABLE TORSION THEORIES AND THE INJECTIVE HULLS OF SIMPLE MODULES”. International Electronic Journal of Algebra, c. 16, sy. 16, 2014, ss. 89-98, doi:10.24330/ieja.266229.
Vancouver Hatipoğlu C. STABLE TORSION THEORIES AND THE INJECTIVE HULLS OF SIMPLE MODULES. IEJA. 2014;16(16):89-98.

Cited By

Injective Hulls of Simple Modules over Differential Operator Rings
Communications in Algebra
Paula A. A. B. Carvalho
https://doi.org/10.1080/00927872.2014.941469