2 citations · 3 across the 5 of their papers we have counts for
6 papers
Generalized Quaternion Rings over for an odd
J. M. Grau, C. Miguel, A. M. oller-Marcén
We consider a generalization of the quaternion ring over a commutative unital ring that includes the case when and are not units of . In th…
On the Diameter of the Commuting Graph of a Full Matrix Ring over a Division Ring
C. Miguel
For a division ring D, finite dimensional over its center F, we give a condiction for the connectedness of the commuting graph of a matrix ring over . Furthermore, we prove that…
On the zero divisor graphs of the ring of Lipschitz integers modulo
Jose Maria Grau, Celino Miquel, Antonio Oller-Marcen
This article studies the zero divisor graphs of the ring of Lipschitz integers modulo . In particular we focus on the number of vertices, the diameter and the girth. We also giv…
A note on commuting graphs of matrix rings over fields
C. Miguel
We will give a short proof of the fact that if the algebraic closure of a field is a finite extension, then for the commuting graph is con…
On the structure of quaternion rings over
Jose Maria Grau, Celino Miquel, Antonio Oller-marcen
In this paper we investigate the structure of , the quaternion rings over . It is proved that these rings are isomorphic to $\left(\frac{-1,-…
A Note on a Conjecture about Commuting Graphs
C. Miguel
We prove that the diameter of the commuting graph of the full ma- trix ring over the real numbers is at most five. This answers, in the affir- mative, a conjecture proposed by Akba…