TY  - Type of reference 
TI  - Une nouvelle caractérisation des anneaux semi-réguliers commutatifs 
AU  - Peter Danchev 
AU  - Mahdi Samiei 
AB  - A commutative ring R is called J-rad clean in case, for any r ∈ R, there is an idempotent e ∈ R such that r−e ∈ U(R) and re ∈ J(R), where U(R) and J(R) denote the set of units and the Jacobson radical of R, respectively. Also, a ring R is called semiregular if R/J(R) is regular in the sense of von Neumann and idempotents lift modulo J(R). We demonstrate that these two concepts are, actually, equivalent and we portray a portion of the properties of this class of rings. In particular, as a direct application, we prove that the commutative group ring RG is J-rad clean if, and only if, R is a commutative J-rad clean ring and G is a torsion abelian group, provided that J(R) is nil. 
DO  - 10.21494/ISTE.OP.2020.0552 
JF  - Avancées en Mathématiques Pures et Appliquées 
KW  - Semiregular rings,  J-clean rings,  J-rad clean rings, Semiregular rings,  J-clean rings,  J-rad clean rings,  
L1  - http://www.openscience.fr/IMG/pdf/iste_apam20v11n1_2.pdf 
LA  - fr 
PB  - ISTE OpenScience 
DA  - 2020/07/3 
SN  - 1869-6090 
TT  - A new characterization of commutative semiregular rings 
UR  - http://www.openscience.fr/Une-nouvelle-caracterisation-des-anneaux-semi-reguliers-commutatifs 
IS  - Numéro 1 (Mai 2020) 
VL  - 11 
ER  -