Locally projective and locally injective modules II
Other Title(s)
المودولات الإسقاطية المحلية و الأفقية المحلية (II)
Author
Source
Damascus University Journal for the Basic Sciences
Issue
Vol. 29, Issue 1 (30 Jun. 2013), pp.11-23, 13 p.
Publisher
Publication Date
2013-06-30
Country of Publication
Syria
No. of Pages
13
Main Subjects
Abstract EN
The object of this paper is to study the locally projective and locally injective modules.
Specifically, this paper is a continuation of study of locally projective and locally injective modules, where a new description of locally projective and locally injective modules is obtained.
The main obtained results include: 1) Let PR be a module.
The following conditions are equivalent: (1) P is a locally projective module.
(2) Tot[M,P] = ∇[M, P] for all M e mod - R.
(3) Tot[P,M] = ∇ [P,M] for all M e mod - R.
(4) [P, M ] is a ∇ — semipotent for all M e mod — R .
(5) [M, P ] is a ∇ — semipotent for all M e mod — R .
2) Let QR be a module.
The following conditions are equivalent: (1) Q is a locally injective module.
(2) Tot[Q, N] = Δ[Q, N] for all N e mod — R.
(3) Tot[N, Q] = Δ[N, Q] for all N e mod — R.
(4) [Q, N] is a Δ — semipotent for all N e mod — R .
(5) [ N, Q] is a Δ — semipotent for all N e mod — R .
3) The following conditions are equivalent for any ring R : (1) Every moduleM e mod — R with EM is a Δ — semipotent ring, is injective.
(2) R — is a semi-simple Artinian ring.
(3) Every module M e mod — R with EM is a ∇ — semipotent ring, is projective.
American Psychological Association (APA)
Hakimi, Hamzah. 2013. Locally projective and locally injective modules II. Damascus University Journal for the Basic Sciences،Vol. 29, no. 1, pp.11-23.
https://search.emarefa.net/detail/BIM-745429
Modern Language Association (MLA)
Hakimi, Hamzah. Locally projective and locally injective modules II. Damascus University Journal for the Basic Sciences Vol. 29, no. 1 (2013), pp.11-23.
https://search.emarefa.net/detail/BIM-745429
American Medical Association (AMA)
Hakimi, Hamzah. Locally projective and locally injective modules II. Damascus University Journal for the Basic Sciences. 2013. Vol. 29, no. 1, pp.11-23.
https://search.emarefa.net/detail/BIM-745429
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 23
Record ID
BIM-745429