Some Results on Triangular Coefficient Matrix Rings

2025/07/20 by Danchev, Peter, Karamali, Gholamreza, Hosseinnezhad, Hessam +1
#16N40 #16S36 #16S50 #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2507.14930

Abstract

In this paper, we introduce the concept of a \it triangular coefficient matrix ring and investigate the structure of its ideals. We then characterize the radicals of the ring \( R_h[x]/⟨ xⁿ ⟩ \) for every positive integer \( n \), where \( R_h[x] \) denotes the Hurwitz polynomial ring and \( ⟨ xⁿ ⟩ \) represents the ideal of this ring generated by \( xⁿ \). Furthermore, we explore several properties that are transferred between the base ring \( R \) and the matrix ring \( H_n(R) \) which is a proper subring of the triangular coefficient matrix ring.

Citations

• Nil clean rings

Related

• Polynomial functions on upper triangular matrix algebras
• Extensions of McCoy Rings
• Jordan derivations on triangular matrix rings
• Isomorphisms between strongly triangular matrix rings
• On a generalization of McCoy Rings