Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
precover; cover; (pre)cover class of modules; hereditary torsion theory; relatively injective modules
precover; cover; (pre)cover class of modules; hereditary torsion theory; relatively injective modules
Summary:
Let $\mathcal G$ be an abstract class (closed under isomorpic copies) of left $R$-modules. In the first part of the paper some sufficient conditions under which $\mathcal G$ is a precover class are given. The next section studies the $\mathcal G$-precovers which are $\mathcal G$-covers. In the final part the results obtained are applied to the hereditary torsion theories on the category on left $R$-modules. Especially, several sufficient conditions for the existence of $\sigma $-torsionfree and $\sigma $-torsionfree $\sigma $-injective covers are presented.
References:
[1] L. Bican, T. Kepka and P. Němec: Rings, Modules, and Preradicals. Marcel Dekker, New York, 1982. MR 0655412
[2] E. Enochs: Torsion free covering modules II. Proc. Amer. Math. Soc. 114 (1963), 884–889. DOI 10.1090/S0002-9939-1963-0168617-7 | MR 0168617
[3] J. Golan: Torsion Theories. Pitman Monographs and Surveys in Pure an Applied Matematics, vol. 29, Longman Scientific and Technical, 1986. MR 0880019 | Zbl 0657.16017
[4] J. R. García Rozas and B. Torrecillas: On the existence of covers by injective modules relative to a torsion theory. Comm. Algebra 24 (1996), 1737–1748. DOI 10.1080/00927879608825667 | MR 1386494
[5] J. Rada and M. Saorín: Rings characterized by (pre)envelopes and (pre)covers of their modules. Comm. Algebra 26 (1998), 899–912. DOI 10.1080/00927879808826172 | MR 1606190
[6] M. Teply: Torsionfree injective modules. Pacific J. Math. 28 (1969), 441–453. DOI 10.2140/pjm.1969.28.441 | MR 0242878
[7] M. Teply: Torsion-free covers II. Israel J. Math. 23 (1976), 132–136. DOI 10.1007/BF02756792 | MR 0417245 | Zbl 0321.16014
[8] B. Torrecillas: T-torsionfree T-injective covers. Comm. Algebra 12 (1984), 2707–2726. DOI 10.1080/00927878408823128 | MR 0757788
[9] J. Xu: Flat Covers of Modules. Lecture Notes in Mathematics, 1634 Springer Verlag, Berlin-Heidelberg-New York, 1996. MR 1438789 | Zbl 0860.16002
Search
Partner of
