A decomposition theorem for semiprime rings

A decomposition theorem for semiprime rings

A ring \(A\) is called an \(FDI\)-ring if there exists a decomposition of the identity of \(A\) in a sum of finite number of pairwise orthogonal primitive idempotents. We call a primitive idempotent \(e\) artinian if the ring \(eAe\) is Artinian. We prove that every semiprime \(FDI\)-ring is a direc...

Full description

Saved in:
Bibliographic Details
Date:2018
Main Author: Khibina, Marina
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
Subjects:
minor of a ring
local idempotent
semiprime ring
Peirce decomposition
16P40
16G10
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/916
Tags: Add Tag
No Tags, Be the first to tag this record!
Journal Title:Algebra and Discrete Mathematics

Institution

Algebra and Discrete Mathematics
id admjournalluguniveduua-article-916
record_format ojs
spelling admjournalluguniveduua-article-9162018-03-21T07:18:38Z A decomposition theorem for semiprime rings Khibina, Marina minor of a ring, local idempotent, semiprime ring, Peirce decomposition 16P40, 16G10 A ring \(A\) is called an \(FDI\)-ring if there exists a decomposition of the identity of \(A\) in a sum of finite number of pairwise orthogonal primitive idempotents. We call a primitive idempotent \(e\) artinian if the ring \(eAe\) is Artinian. We prove that every semiprime \(FDI\)-ring is a direct product of a semisimple Artinian ring and a semiprime \(FDI\)-ring whose identity decomposition doesn't contain artinian idempotents. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/916 Algebra and Discrete Mathematics; Vol 4, No 1 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/916/445 Copyright (c) 2018 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2018-03-21T07:18:38Z
collection OJS
language English
topic minor of a ring
local idempotent
semiprime ring
Peirce decomposition
16P40
16G10
spellingShingle minor of a ring
local idempotent
semiprime ring
Peirce decomposition
16P40
16G10
Khibina, Marina
A decomposition theorem for semiprime rings
topic_facet minor of a ring
local idempotent
semiprime ring
Peirce decomposition
16P40
16G10
format Article
author Khibina, Marina
author_facet Khibina, Marina
author_sort Khibina, Marina
title A decomposition theorem for semiprime rings
title_short A decomposition theorem for semiprime rings
title_full A decomposition theorem for semiprime rings
title_fullStr A decomposition theorem for semiprime rings
title_full_unstemmed A decomposition theorem for semiprime rings
title_sort decomposition theorem for semiprime rings
description A ring \(A\) is called an \(FDI\)-ring if there exists a decomposition of the identity of \(A\) in a sum of finite number of pairwise orthogonal primitive idempotents. We call a primitive idempotent \(e\) artinian if the ring \(eAe\) is Artinian. We prove that every semiprime \(FDI\)-ring is a direct product of a semisimple Artinian ring and a semiprime \(FDI\)-ring whose identity decomposition doesn't contain artinian idempotents.
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/916
work_keys_str_mv AT khibinamarina adecompositiontheoremforsemiprimerings
AT khibinamarina decompositiontheoremforsemiprimerings
first_indexed 2025-12-02T15:41:25Z
last_indexed 2025-12-02T15:41:25Z
_version_ 1850412194196357120

Similar Items