On some radicals and proper classes associated to simple modules
On some radicals and proper classes associated to simple modules
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.
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- [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.