TY - Type of reference
TI - A new characterization of commutative semiregular rings
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.2020.0542
JF - Advances in Pure and Applied Mathematics
KW - Semiregular rings, J-clean rings, J-rad clean rings, Semiregular rings, J-clean rings, J-rad clean rings,
L1 - http://openscience.fr/IMG/pdf/iste_apam20v11n1_2.pdf
LA - en
PB - ISTE OpenScience
DA - 2020/07/3
SN - 1869-6090
TT - Une nouvelle caractérisation des anneaux semi-réguliers commutatifs
UR - http://openscience.fr/A-new-characterization-of-commutative-semiregular-rings
IS - Issue 1 (May 2020)
VL - 11
ER -