Algebraic Properties of Semi-Direct Sums of Rings

Marta Nowakowska

doi:10.2478/amsil-2025-0012

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Algebraic Properties of Semi-Direct Sums of Rings

Annales Mathematicae Silesianae

Volume 39 (2025): Issue 2 (September 2025)

By: Marta Nowakowska

Open Access

|Jun 2025

Abstract

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}.

The aim of this paper is to investigate certain algebraic properties of semidirect sums of associative rings with applications to amalgamated rings. We generalize several results from the literature to associative rings without unity. In particular we show that the class of semi-direct sums of rings is equal to the class of amalgamated rings, we provide a description of the Jacobson radical of semi-direct sums and we offer a characterization of semi-direct sums that are left Steinitz rings.

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2025-0012 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 319 - 330

Submitted on: Feb 2, 2025

Accepted on: May 7, 2025

Published on: Jun 2, 2025

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

16L30,

16N20,

16S70,

16S99

Related subjects:

Mathematics,

General mathematics

© 2025 Marta Nowakowska, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 39 (2025): Issue 2 (September 2025)