τ-INJECTIVE SUBMODULES OF INDECOMPOSABLE INJECTIVE MODULES

Title & Authors
τ-INJECTIVE SUBMODULES OF INDECOMPOSABLE INJECTIVE MODULES
CRIVEI SEPTIMIU;

Abstract
Let $\small{\tau}$ be a hereditary torsion theory and let p be a prime ideal of a commutative ring R. We study the existence of (minimal) $\small{\tau-injective}$ submodules of the injective hull of R/p.
Keywords
hereditary torsiion theory;($\small{\tau}$-)injective hull;
Language
English
Cited by
1.
Change of ring and torsion-theoretic injectivity, Bulletin of the Australian Mathematical Society, 2007, 75, 01, 127
References
1.
T. Albu, G. Krause and M. L. Teply, Bijective relative Gabriel correspondence over rings with torsion theoretic Krull dimension, J. Algebra 243 (2001), no. 2, 644-674

2.
S. Crivei, On m-injective modules over noetherian rings, Pure Math. Appl. 11 (2000), no. 2, 173-181

3.
S. Crivei, Injective modules relative to the Dickson torsion theory, Vietnam J. Math. 29 (2001), no. 4, 369-378

4.
S. Crivei, On $\tau$--injective hulls of modules, Publ. Math. Debrecen 61 (2002), no. 1-2, 145-155

5.
S. Crivei, On $\tau$-completely decomposable modules, Bull. Austral. Math. Soc. 70 (2004), no. 1, 163-175

6.
S. E. Dickson, A torsion theory for abelian categories, Trans. Amer. Math. Soc. 121 (1966), 223-235

7.
B. Eckmann and A. Schopf, Uber injektive Moduln, Arch. Math. 4 (1953), 75-78

8.
C. Faith, On the structure of indecomposable injective modules, Comm. Algebra 2 (1974), 559-571

9.
C. Faith, Indecomposable injective modules and a theorem of Kaplansky, Comm. Algebra 30 (2002), no. 12, 5875-5889

10.
C. Faith and E. Walker, Direct sum representations of injective modules, J. Al-gebra 5 (1967), 203-221

11.
J. S. Golan, Torsion theories, Pitman Monographs and Surveys in Pure and Applied Mathematics, 29. Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1986

12.
Y. Hirano, On injective hulls of simple modules, J. Algebra 225 (2000), no. 1, 299-308

13.
P. Kim and G. Krause, Local bijective Gabriel correspondence and relative fully boundedness in $\tau$-noetherian rings, Comm. Algebra 27 (1999), no. 7, 3339-3351

14.
T. G. Kucera, Explicit description of injective envelopes: Generalizations of a result of Northcott, Comm. Algebra 17 (1989), no. 11, 2703-2715

15.
S. C. Lee, Direct sum decompositions of indecomposable injective modules, Bull. Korean Math. Soc. 35 (1998), no. 1, 33-43

16.
K. Masaike and T. Horigome, Direct sum of $\tau$-injective modules, Tsukuba J. Math. 4 (1980), no. 1, 77-81

17.
E. Matlis, Injective modules over noetherian rings, Pacific J. Math. 8 (1958), 511-528

18.
S. Mohamed and S. Singh, Decomposition of $\sigma$-injective modules, Comm. Algebra 9 (1981), no. 6, 601-611

19.
D. G. Northcott, Injective envelopes and inverse polynomials, J. London Math. Soc.(2) 8 (1974), 290-296

20.
D. W. Sharpe and P. Vamos, Injective modules, Cambridge University Press, London-New York, 1972

21.
B. Stenstrom, Rings of quotients Die Grundlehren der Mathematischen Wis-senschaften, Springer-Verlag, New York-Heidelberg, 1975

22.
J. Xu, Flat covers of modules, Lecture Notes in Mathematics, 1634. Springer-Verlag, Berlin, 1996