I-Rad-⊕-supplemented modules-Reference-Cited by-同舟云学术

I-Rad-⊕-supplemented modules

Published:2019-08-01 Issue:1 Volume:11 Page:224-233
ISSN:2066-7752
Container-title:Acta Universitatis Sapientiae, Mathematica
language:en
Short-container-title:

Author:

Türkmen Burcu Nişancı¹

Affiliation:

1. Faculty of Art and Science , Amasya University , Ipekköy, Amasya , Turkey

Abstract

Abstract Let M be an R-module and I be an ideal of R. We say that M is I-Rad-⊕-supplemented, provided for every submodule N of M, there exists a direct summand K of M such that M = N + K, N ∩ K ⊆ IK and N ∩ K Rad(K). The aim of this paper is to show new properties of I-Rad-⊕-supplemented modules. Especially, we show that any finite direct sum of I-Rad-⊕-supplemented modules is I-Rad-⊕-supplemented. We also prove that an R-module M is I-Rad-⊕-supplemented if and only if K and

M K

${M \over K}$

are I-Rad-⊕-supplemented for a fully invariant direct summand K of M. Finally, we determine the structure of I-Rad-⊕-supplemented modules over a discrete valuation ring.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.sciendo.com/pdf/10.2478/ausm-2019-0017

Reference18 articles.

1. [1] F. W. Anderson, K. R. Fuller, Rings and Categories of Modules, Springer-Verlag, 1992.10.1007/978-1-4612-4418-9

2. [2] M. F. Atiyah, I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, London, 1969.

3. [3] E. Büyükaşık, Yılmaz M. Demirci, Weakly Distributive Modules. Applications to Supplement Submodules, Proc. Indian Acad. Sci. (Math. Sci.), 120 (5), (2010), 525–534.10.1007/s12044-010-0053-9

4. [4] J. Clark, C. Lomp, N. Vanaja, R. Wisbauer, Lifting Modules. Supplements and Projectivity in Module Theory, Frontiers in Mathematics, Birkhäuser, Basel, 2006.

5. [5] H. Çalışıcı, E. Türkmen, Generalized ⊕-supplemented modules, Algebra and Discrete Mathematics, 10 (2) (2010), 10–18.