2024/04/24 by Nazemian, Zahra
#16E50 #16P10 #16S99 #FOS: Mathematics #Primary 16D70 #Representation Theory (math.RT) #Secondary 16D40
paper · doi:10.48550/arxiv.2404.15769
For every infinite cardinal number κ, κ-monoids and their realization have recently been introduced and studied by Nazemian and Smertnig. A κ-monoid H has a realization to a ring R if there exists an element x ∈ H such that H is ℵ1 --braided over add(ℵ0 x), and add(ℵ0 x), as ℵ0-monoid, has a realization to R. Furthermore, H has a realization to hereditary rings if there exists an element x ∈ H such that H is braided over add(x). These prompt an investigation into when ℵ0-monoids have realizations. In this paper, we discuss the realization of ℵ0-monoids and provide a complete characterization for the realization of two-generated ones in hereditary Von Neumann regular rings.