JOURNAL BROWSE
Search
Advanced SearchSearch Tips
τ-INJECTIVE SUBMODULES OF INDECOMPOSABLE INJECTIVE MODULES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
τ-INJECTIVE SUBMODULES OF INDECOMPOSABLE INJECTIVE MODULES
CRIVEI SEPTIMIU;
  PDF(new window)
 Abstract
Let be a hereditary torsion theory and let p be a prime ideal of a commutative ring R. We study the existence of (minimal) submodules of the injective hull of R/p.
 Keywords
hereditary torsiion theory;(-)injective hull;
 Language
English
 Cited by
1.
Change of ring and torsion-theoretic injectivity, Bulletin of the Australian Mathematical Society, 2007, 75, 01, 127  crossref(new windwow)
 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 crossref(new window)

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 crossref(new window)

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

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

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

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

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

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 crossref(new window)

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 crossref(new window)

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

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 crossref(new window)

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

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

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