Rings in which elements are sum of a central element and an element in the Jacobson radical

Guanglin Ma; Yao Wang; André Leroy

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 2, page 515-533
  • ISSN: 0011-4642

Abstract

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An element in a ring R is called CJ if it is of the form c + j , where c belongs to the center and j is an element from the Jacobson radical. A ring R is called CJ if each element of R is CJ. We establish the basic properties of CJ rings, give several characterizations of these rings, and connect this notion with many standard elementwise properties such as clean, uniquely clean, nil clean, CN, and CU. We study the behavior of this notion under various ring extensions. In particular, we show that the subring C + J is always a CJ ring and that if R [ x ] is a CJ ring then R satisfies the Köthe conjecture.

How to cite

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Ma, Guanglin, Wang, Yao, and Leroy, André. "Rings in which elements are sum of a central element and an element in the Jacobson radical." Czechoslovak Mathematical Journal 74.2 (2024): 515-533. <http://eudml.org/doc/299447>.

@article{Ma2024,
abstract = {An element in a ring $R$ is called CJ if it is of the form $c+j$, where $c$ belongs to the center and $j$ is an element from the Jacobson radical. A ring $R$ is called CJ if each element of $R$ is CJ. We establish the basic properties of CJ rings, give several characterizations of these rings, and connect this notion with many standard elementwise properties such as clean, uniquely clean, nil clean, CN, and CU. We study the behavior of this notion under various ring extensions. In particular, we show that the subring $C+J$ is always a CJ ring and that if $R[x]$ is a CJ ring then $R$ satisfies the Köthe conjecture.},
author = {Ma, Guanglin, Wang, Yao, Leroy, André},
journal = {Czechoslovak Mathematical Journal},
keywords = {CJ ring; center; Jacobson radical; clean ring},
language = {eng},
number = {2},
pages = {515-533},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Rings in which elements are sum of a central element and an element in the Jacobson radical},
url = {http://eudml.org/doc/299447},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Ma, Guanglin
AU - Wang, Yao
AU - Leroy, André
TI - Rings in which elements are sum of a central element and an element in the Jacobson radical
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 2
SP - 515
EP - 533
AB - An element in a ring $R$ is called CJ if it is of the form $c+j$, where $c$ belongs to the center and $j$ is an element from the Jacobson radical. A ring $R$ is called CJ if each element of $R$ is CJ. We establish the basic properties of CJ rings, give several characterizations of these rings, and connect this notion with many standard elementwise properties such as clean, uniquely clean, nil clean, CN, and CU. We study the behavior of this notion under various ring extensions. In particular, we show that the subring $C+J$ is always a CJ ring and that if $R[x]$ is a CJ ring then $R$ satisfies the Köthe conjecture.
LA - eng
KW - CJ ring; center; Jacobson radical; clean ring
UR - http://eudml.org/doc/299447
ER -

References

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