Module decompositions via Rickart modules

This work is devoted to the investigation of module decompositions which arise from Rickart modules, socle and radical of modules. In this regard, the structure and several illustrative examples of inverse split modules relative to the socle and radical are given. It is shown that a module M has dec...

Full description

Saved in:
Bibliographic Details
Published in:Algebra and Discrete Mathematics
Date:2018
Main Authors: Harmanci, A., Ungor, B.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2018
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/188373
Tags: Add Tag
No Tags, Be the first to tag this record!
Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Module decompositions via Rickart modules/ A. Harmanci, B. Ungor // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 1. — С. 47–64. — Бібліогр.: 15 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-188373
record_format dspace
spelling Harmanci, A.
Ungor, B.
2023-02-26T12:20:21Z
2023-02-26T12:20:21Z
2018
Module decompositions via Rickart modules/ A. Harmanci, B. Ungor // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 1. — С. 47–64. — Бібліогр.: 15 назв. — англ.
1726-3255
2010 MSC: 16D10, 16D40, 16D80.
https://nasplib.isofts.kiev.ua/handle/123456789/188373
This work is devoted to the investigation of module decompositions which arise from Rickart modules, socle and radical of modules. In this regard, the structure and several illustrative examples of inverse split modules relative to the socle and radical are given. It is shown that a module M has decompositions M = Soc(M) ⊕ N and M = Rad(M) ⊕ K where N and K are Rickart if and only if M is Soc(M)-inverse split and Rad(M)-inverse split, respectively. Right Soc(·)-inverse split left perfect rings and semiprimitive right hereditary rings are determined exactly. Also, some characterizations for a ring R which has a decomposition R = Soc(RR) ⊕ I with I a hereditary Rickart module are obtained.
The authors are very thankful to the referee for his/her helpful suggestions to improve the presentation of this paper.
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
Module decompositions via Rickart modules
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Module decompositions via Rickart modules
spellingShingle Module decompositions via Rickart modules
Harmanci, A.
Ungor, B.
title_short Module decompositions via Rickart modules
title_full Module decompositions via Rickart modules
title_fullStr Module decompositions via Rickart modules
title_full_unstemmed Module decompositions via Rickart modules
title_sort module decompositions via rickart modules
author Harmanci, A.
Ungor, B.
author_facet Harmanci, A.
Ungor, B.
publishDate 2018
language English
container_title Algebra and Discrete Mathematics
publisher Інститут прикладної математики і механіки НАН України
format Article
description This work is devoted to the investigation of module decompositions which arise from Rickart modules, socle and radical of modules. In this regard, the structure and several illustrative examples of inverse split modules relative to the socle and radical are given. It is shown that a module M has decompositions M = Soc(M) ⊕ N and M = Rad(M) ⊕ K where N and K are Rickart if and only if M is Soc(M)-inverse split and Rad(M)-inverse split, respectively. Right Soc(·)-inverse split left perfect rings and semiprimitive right hereditary rings are determined exactly. Also, some characterizations for a ring R which has a decomposition R = Soc(RR) ⊕ I with I a hereditary Rickart module are obtained.
issn 1726-3255
url https://nasplib.isofts.kiev.ua/handle/123456789/188373
fulltext
citation_txt Module decompositions via Rickart modules/ A. Harmanci, B. Ungor // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 1. — С. 47–64. — Бібліогр.: 15 назв. — англ.
work_keys_str_mv AT harmancia moduledecompositionsviarickartmodules
AT ungorb moduledecompositionsviarickartmodules
first_indexed 2025-11-26T00:41:48Z
last_indexed 2025-11-26T00:41:48Z
_version_ 1850600479814320128