A generalization of reflexive rings

Çalcı, Mete Burak, Chen, Huanyin, and Halıcıoğlu, Sait. "A generalization of reflexive rings." Mathematica Bohemica 149.2 (2024): 225-235. <http://eudml.org/doc/299431>.

@article{Çalcı2024,
abstract = {We introduce a class of rings which is a generalization of reflexive rings and $J$-reversible rings. Let $R$ be a ring with identity and $J(R)$ denote the Jacobson radical of $R$. A ring $R$ is called $J$-reflexive if for any $a, b \in R$, $aRb = 0$ implies $bRa \subseteq J(R)$. We give some characterizations of a $J$-reflexive ring. We prove that some results of reflexive rings can be extended to $J$-reflexive rings for this general setting. We conclude some relations between $J$-reflexive rings and some related rings. We investigate some extensions of a ring which satisfies the $J$-reflexive property and we show that the $J$-reflexive property is Morita invariant.},
author = {Çalcı, Mete Burak, Chen, Huanyin, Halıcıoğlu, Sait},
journal = {Mathematica Bohemica},
keywords = {reflexive ring; reversible ring; $J$-reflexive ring; $J$-reversible ring; ring extension},
language = {eng},
number = {2},
pages = {225-235},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A generalization of reflexive rings},
url = {http://eudml.org/doc/299431},
volume = {149},
year = {2024},
}

TY - JOUR
AU - Çalcı, Mete Burak
AU - Chen, Huanyin
AU - Halıcıoğlu, Sait
TI - A generalization of reflexive rings
JO - Mathematica Bohemica
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 149
IS - 2
SP - 225
EP - 235
AB - We introduce a class of rings which is a generalization of reflexive rings and $J$-reversible rings. Let $R$ be a ring with identity and $J(R)$ denote the Jacobson radical of $R$. A ring $R$ is called $J$-reflexive if for any $a, b \in R$, $aRb = 0$ implies $bRa \subseteq J(R)$. We give some characterizations of a $J$-reflexive ring. We prove that some results of reflexive rings can be extended to $J$-reflexive rings for this general setting. We conclude some relations between $J$-reflexive rings and some related rings. We investigate some extensions of a ring which satisfies the $J$-reflexive property and we show that the $J$-reflexive property is Morita invariant.
LA - eng
KW - reflexive ring; reversible ring; $J$-reflexive ring; $J$-reversible ring; ring extension
UR - http://eudml.org/doc/299431
ER -