Algebraic Properties of Semi-Direct Sums of Rings

Let R be an associative ring not necessarily with unity. We say that R is a semi-direct sum of rings S and I, if R = S + I, where S is a subring of a ring R, I is an ideal of R and S ∩ I = {0}.

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Main Author: Nowakowska Marta
Format: Article
Language:English
Published: Sciendo 2025-06-01
Series:Annales Mathematicae Silesianae
Subjects:
Online Access:https://doi.org/10.2478/amsil-2025-0012
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author Nowakowska Marta
author_facet Nowakowska Marta
author_sort Nowakowska Marta
collection DOAJ
description Let R be an associative ring not necessarily with unity. We say that R is a semi-direct sum of rings S and I, if R = S + I, where S is a subring of a ring R, I is an ideal of R and S ∩ I = {0}.
format Article
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institution Kabale University
issn 2391-4238
language English
publishDate 2025-06-01
publisher Sciendo
record_format Article
series Annales Mathematicae Silesianae
spelling doaj-art-71e75f89361c43ccb10e0e3f5d49c3622025-08-20T03:51:24ZengSciendoAnnales Mathematicae Silesianae2391-42382025-06-0139231933010.2478/amsil-2025-0012Algebraic Properties of Semi-Direct Sums of RingsNowakowska Marta0University of Silesia in Katowice, Katowice, PolandLet R be an associative ring not necessarily with unity. We say that R is a semi-direct sum of rings S and I, if R = S + I, where S is a subring of a ring R, I is an ideal of R and S ∩ I = {0}.https://doi.org/10.2478/amsil-2025-001216l3016n2016s7016s99semi-direct sumamalgamated ringjacobson radicalleft steinitz ringuniquely clean ringlocal ring
spellingShingle Nowakowska Marta
Algebraic Properties of Semi-Direct Sums of Rings
Annales Mathematicae Silesianae
16l30
16n20
16s70
16s99
semi-direct sum
amalgamated ring
jacobson radical
left steinitz ring
uniquely clean ring
local ring
title Algebraic Properties of Semi-Direct Sums of Rings
title_full Algebraic Properties of Semi-Direct Sums of Rings
title_fullStr Algebraic Properties of Semi-Direct Sums of Rings
title_full_unstemmed Algebraic Properties of Semi-Direct Sums of Rings
title_short Algebraic Properties of Semi-Direct Sums of Rings
title_sort algebraic properties of semi direct sums of rings
topic 16l30
16n20
16s70
16s99
semi-direct sum
amalgamated ring
jacobson radical
left steinitz ring
uniquely clean ring
local ring
url https://doi.org/10.2478/amsil-2025-0012
work_keys_str_mv AT nowakowskamarta algebraicpropertiesofsemidirectsumsofrings