2024/02/29 by Grigore Călugăreanu, Călugăreanu, Grigore, Tsiu‐Kwen Lee +3 · 1 citation
Mathematics · #16N60 #16S50 #16U10 #16U40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2402.19374
openalex publication_date 2024/02/29 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
For a nonempty subset X of a ring R, the ring R is called X-semiprime if, given a∈ R, aXa=0 implies a=0. This provides a proper class of semiprime rings. First, we clarify the relationship between idempotent semiprime and unit-semiprime rings. Secondly, given a Lie ideal L of a ring R, we offer a criterion for R to be L-semiprime. For a prime ring R, we characterizes Lie ideals L of R such that R is L-semiprime. Moreover, X-semiprimeness of matrix rings, prime rings (with a nontrivial idempotent), semiprime rings, regular rings, and subdirect products are studied.