<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>A ring is called <italic>negative clean</italic> if the negative (i.e., the additive inverse) of each clean element is also clean. Clean rings are negative clean.</p>
<p>In this paper, we develop the theory of the negative rings, with special emphasis on finding the clean matrices which have (or have not) clean negatives. Many explicit results are proved for 2 × 2 matrices and some hard to solve quadratic Diophantive equations are displayed.</p>
</abstract>

A ring is called negative clean if the negative (i.e., the additive inverse) of each clean element is also clean. Clean rings are negative clean.
In this paper, we develop the theory of the negative rings, with special emphasis on finding the clean matrices which have (or have not) clean negatives. Many explicit results are proved for 2 × 2 matrices and some hard to solve quadratic Diophantive equations are displayed.

Negative clean rings

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Negative clean rings"}

A ring is called negative clean if the negative (i.e., the additive inverse) of each clean element is also clean. Clean rings are negative clean.
In this...

Negative clean rings

Published Online: Jun 02, 2022

Page range: 63 - 89

Received: Jun 09, 2021

Accepted: Oct 10, 2021

DOI: https://doi.org/10.2478/auom-2022-0019

Keywords
clean ring, negative clean ring, strongly clean element, 2 × 2 matrix

© 2022 Grigore Călugăreanu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Negative clean rings

Published Online: Jun 02, 2022

Page range: 63 - 89

Received: Jun 09, 2021

Accepted: Oct 10, 2021

DOI: https://doi.org/10.2478/auom-2022-0019

Keywordsclean ring, negative clean ring, strongly clean element, 2 × 2 matrix

© 2022 Grigore Călugăreanu et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
clean ring, negative clean ring, strongly clean element, 2 × 2 matrix