2025/01/02 by Omid Hasanzadeh, Hasanzadeh, Omid, A. Moussavi +3
Mathematics · #16S34 #16U60 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2501.04720
openalex publication_date 2025/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Rings in which the square of each unit lies in 1+Δ(R), are said to be 2-ΔU, where J(R)⊆Δ(R) =: \r ∈ R | r + U(R) ⊆ U(R)\. The set Δ(R) is the largest Jacobson radical subring of R which is closed with respect to multiplication by units of R and is studied in \cite2. The class of 2-ΔU rings consists several rings including UJ-rings, 2-UJ rings and ΔU-rings, and we observe that ΔU-rings are UUC. The structure of 2-ΔU rings is studied under various conditions. Moreover, the 2-ΔU property is studied under some algebraic constructions.