Rings in which the square of a unit is the sum of 1 and an element from $\sqrt{J(R)}$
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914331690532864 |
|---|---|
| author | Udar, Dinesh Saini, Shiksha |
| author_facet | Udar, Dinesh Saini, Shiksha |
| contents | Through this paper, we study the rings in which every unit's square is an element of the set $1+\sqrt{J(R)}$, and call them $2-\sqrt{J}U$ rings. Here, $\sqrt{J(R)}=\{x \in R: x^m \in J(R)$ for some $m \geq 1 \}$. We show that every $UU,~UJ,~2-UU,~2-UJ$ and $\sqrt{J}U$ ring is a $2-\sqrt{J}U$ ring. After exploring the basic properties, we show that the corner ring and unit closed subring of a $2-\sqrt{J}U$ ring are also $2-\sqrt{J}U$ rings. The ring of all $n\times n$ matrix rings for any $n>1$ is never a $2-\sqrt{J}U$ ring. We have focused on several other matrix extensions and group rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14521 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rings in which the square of a unit is the sum of 1 and an element from $\sqrt{J(R)}$ Udar, Dinesh Saini, Shiksha Rings and Algebras Through this paper, we study the rings in which every unit's square is an element of the set $1+\sqrt{J(R)}$, and call them $2-\sqrt{J}U$ rings. Here, $\sqrt{J(R)}=\{x \in R: x^m \in J(R)$ for some $m \geq 1 \}$. We show that every $UU,~UJ,~2-UU,~2-UJ$ and $\sqrt{J}U$ ring is a $2-\sqrt{J}U$ ring. After exploring the basic properties, we show that the corner ring and unit closed subring of a $2-\sqrt{J}U$ ring are also $2-\sqrt{J}U$ rings. The ring of all $n\times n$ matrix rings for any $n>1$ is never a $2-\sqrt{J}U$ ring. We have focused on several other matrix extensions and group rings. |
| title | Rings in which the square of a unit is the sum of 1 and an element from $\sqrt{J(R)}$ |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2602.14521 |