The socle of Leavitt path algebras over a semiprime ring

The socle of Leavitt path algebras over a semiprime ring

The Reduction Theorem in Leavitt path algebra over a commutative unital ring is very important to prove that the Leavitt path algebra is semiprime if and only if the ring is also semiprime. Any minimal ideal in the semiprime ring and line point will construct a left minimal ideal in the Leavitt path...

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Date:2023
Main Author: Wardati, K.
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2023
Subjects:
reduction theorem
semiprime
socle
line point
Primary 16S88
Secondary 16D70
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1850
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id oai:ojs.admjournal.luguniv.edu.ua:article-1850
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spelling oai:ojs.admjournal.luguniv.edu.ua:article-18502023-02-08T16:55:57Z The socle of Leavitt path algebras over a semiprime ring Wardati, K. reduction theorem, semiprime, socle, line point Primary 16S88; Secondary 16D70 The Reduction Theorem in Leavitt path algebra over a commutative unital ring is very important to prove that the Leavitt path algebra is semiprime if and only if the ring is also semiprime. Any minimal ideal in the semiprime ring and line point will construct a left minimal ideal in the Leavitt path algebra. Vice versa, any left minimal ideal in the semiprime Leavitt path algebra can be found both minimal ideal in the semiprime ring and line point that generate it. The socle of semiprime Leavitt path algebra is constructed by minimal ideals of the semiprime ring and the set of all line points. Lugansk National Taras Shevchenko University LPPM UIN Sunan Kalijaga, Cluster of Research Leader, 2019 2023-02-08 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1850 10.12958/adm1850 Algebra and Discrete Mathematics; Vol 34, No 1 (2022) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1850/pdf Copyright (c) 2023 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2023-02-08T16:55:57Z
collection OJS
language English
topic reduction theorem
semiprime
socle
line point
Primary 16S88
Secondary 16D70
spellingShingle reduction theorem
semiprime
socle
line point
Primary 16S88
Secondary 16D70
Wardati, K.
The socle of Leavitt path algebras over a semiprime ring
topic_facet reduction theorem
semiprime
socle
line point
Primary 16S88
Secondary 16D70
format Article
author Wardati, K.
author_facet Wardati, K.
author_sort Wardati, K.
title The socle of Leavitt path algebras over a semiprime ring
title_short The socle of Leavitt path algebras over a semiprime ring
title_full The socle of Leavitt path algebras over a semiprime ring
title_fullStr The socle of Leavitt path algebras over a semiprime ring
title_full_unstemmed The socle of Leavitt path algebras over a semiprime ring
title_sort socle of leavitt path algebras over a semiprime ring
description The Reduction Theorem in Leavitt path algebra over a commutative unital ring is very important to prove that the Leavitt path algebra is semiprime if and only if the ring is also semiprime. Any minimal ideal in the semiprime ring and line point will construct a left minimal ideal in the Leavitt path algebra. Vice versa, any left minimal ideal in the semiprime Leavitt path algebra can be found both minimal ideal in the semiprime ring and line point that generate it. The socle of semiprime Leavitt path algebra is constructed by minimal ideals of the semiprime ring and the set of all line points.
publisher Lugansk National Taras Shevchenko University
publishDate 2023
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1850
work_keys_str_mv AT wardatik thesocleofleavittpathalgebrasoverasemiprimering
AT wardatik socleofleavittpathalgebrasoverasemiprimering
first_indexed 2025-07-17T10:31:04Z
last_indexed 2025-07-17T10:31:04Z
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