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On some radicals and proper classes associated to simple modules

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

Abstract

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.

References

  • [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.
Year 2017, , 123 - 129, 10.01.2017
https://doi.org/10.13069/jacodesmath.284943

Abstract

References

  • [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.
There are 7 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Septimiu Crivei

Derya Keskin Tütüncü

Publication Date January 10, 2017
Published in Issue Year 2017

Cite

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. May 2017;4(2 (Special Issue: Noncommutative rings and their applications):123-129. doi:10.13069/jacodesmath.284943
Chicago Crivei, Septimiu, and Derya Keskin Tütüncü. “On Some Radicals and Proper Classes Associated to Simple Modules”. Journal of Algebra Combinatorics Discrete Structures and Applications 4, no. 2 (Special Issue: Noncommutative rings and their applications) (May 2017): 123-29. https://doi.org/10.13069/jacodesmath.284943.
EndNote Crivei S, Keskin Tütüncü D (May 1, 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 and D. Keskin Tütüncü, “On some radicals and proper classes associated to simple modules”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 4, no. 2 (Special Issue: Noncommutative rings and their applications), pp. 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) (May 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 and Derya Keskin Tütüncü. “On Some Radicals and Proper Classes Associated to Simple Modules”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 4, no. 2 (Special Issue: Noncommutative rings and their applications), 2017, pp. 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.