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On some radicals and proper classes associated to simple modules

Yıl 2017, , 123 - 129, 10.01.2017
https://doi.org/10.13069/jacodesmath.284943

Öz

For a unitary right module $M$, there are two known partitions of
simple modules in the category $\sigma[M]$: the first one divides
them into $M$-injective modules and $M$-small modules, while the
second one divides them into $M$-projective modules and
$M$-singular modules. We study inclusions between the first two
and the last two classes of simple modules in terms of some
associated radicals and proper classes.

Kaynakça

  • [1] K. Al–Takhman, C. Lomp, R. Wisbauer, $\tau-$complemented and $\tau-$supplemented modules, Algebra Discrete Math. 3 (2006) 1–16.
  • [2] D. Buchsbaum, A note on homology in categories, Ann. Math. 69(1) (1959) 66–74.
  • [3] J. Clark, C. Lomp, N. Vanaja, R. Wisbauer, Lifting Modules, Frontiers in Mathematics, Birkhäuser, Basel, 2006.
  • [4] N. V. Dung, D. V. Huynh, P. Smith, R. Wisbauer, Extending Modules, Pitman Research Notes in Mathematics, Harlow, Longman, 1994.
  • [5] C. F. Preisser Montaño, Proper classes of short exact sequences and structure theory of modules, Ph.D. Thesis, Düsseldorf, 2010.
  • [6] B. Stenström, Rings of Quotients, Springer, Berlin, Heidelberg, New York, 1975.
  • [7] Y. Zhou, Generalizations of perfect, semiperfect and semiregular rings, Algebra Colloq. 7(3) (2000) 305–318.
Yıl 2017, , 123 - 129, 10.01.2017
https://doi.org/10.13069/jacodesmath.284943

Öz

Kaynakça

  • [1] K. Al–Takhman, C. Lomp, R. Wisbauer, $\tau-$complemented and $\tau-$supplemented modules, Algebra Discrete Math. 3 (2006) 1–16.
  • [2] D. Buchsbaum, A note on homology in categories, Ann. Math. 69(1) (1959) 66–74.
  • [3] J. Clark, C. Lomp, N. Vanaja, R. Wisbauer, Lifting Modules, Frontiers in Mathematics, Birkhäuser, Basel, 2006.
  • [4] N. V. Dung, D. V. Huynh, P. Smith, R. Wisbauer, Extending Modules, Pitman Research Notes in Mathematics, Harlow, Longman, 1994.
  • [5] C. F. Preisser Montaño, Proper classes of short exact sequences and structure theory of modules, Ph.D. Thesis, Düsseldorf, 2010.
  • [6] B. Stenström, Rings of Quotients, Springer, Berlin, Heidelberg, New York, 1975.
  • [7] Y. Zhou, Generalizations of perfect, semiperfect and semiregular rings, Algebra Colloq. 7(3) (2000) 305–318.
Toplam 7 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Makaleler
Yazarlar

Septimiu Crivei

Derya Keskin Tütüncü

Yayımlanma Tarihi 10 Ocak 2017
Yayımlandığı Sayı Yıl 2017

Kaynak Göster

APA Crivei, S., & Keskin Tütüncü, D. (2017). On some radicals and proper classes associated to simple modules. Journal of Algebra Combinatorics Discrete Structures and Applications, 4(2 (Special Issue: Noncommutative rings and their applications), 123-129. https://doi.org/10.13069/jacodesmath.284943
AMA Crivei S, Keskin Tütüncü D. On some radicals and proper classes associated to simple modules. Journal of Algebra Combinatorics Discrete Structures and Applications. Mayıs 2017;4(2 (Special Issue: Noncommutative rings and their applications):123-129. doi:10.13069/jacodesmath.284943
Chicago Crivei, Septimiu, ve Derya Keskin Tütüncü. “On Some Radicals and Proper Classes Associated to Simple Modules”. Journal of Algebra Combinatorics Discrete Structures and Applications 4, sy. 2 (Special Issue: Noncommutative rings and their applications) (Mayıs 2017): 123-29. https://doi.org/10.13069/jacodesmath.284943.
EndNote Crivei S, Keskin Tütüncü D (01 Mayıs 2017) On some radicals and proper classes associated to simple modules. Journal of Algebra Combinatorics Discrete Structures and Applications 4 2 (Special Issue: Noncommutative rings and their applications) 123–129.
IEEE S. Crivei ve D. Keskin Tütüncü, “On some radicals and proper classes associated to simple modules”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 4, sy. 2 (Special Issue: Noncommutative rings and their applications), ss. 123–129, 2017, doi: 10.13069/jacodesmath.284943.
ISNAD Crivei, Septimiu - Keskin Tütüncü, Derya. “On Some Radicals and Proper Classes Associated to Simple Modules”. Journal of Algebra Combinatorics Discrete Structures and Applications 4/2 (Special Issue: Noncommutative rings and their applications) (Mayıs 2017), 123-129. https://doi.org/10.13069/jacodesmath.284943.
JAMA Crivei S, Keskin Tütüncü D. On some radicals and proper classes associated to simple modules. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017;4:123–129.
MLA Crivei, Septimiu ve Derya Keskin Tütüncü. “On Some Radicals and Proper Classes Associated to Simple Modules”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 4, sy. 2 (Special Issue: Noncommutative rings and their applications), 2017, ss. 123-9, doi:10.13069/jacodesmath.284943.
Vancouver Crivei S, Keskin Tütüncü D. On some radicals and proper classes associated to simple modules. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017;4(2 (Special Issue: Noncommutative rings and their applications):123-9.