9 citations · 36 across the 31 of their papers we have counts for
6 papers · 1 filter
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…
Power sums over commutative and unitary rings
Jose Maria Grau, Antonio. M. Oller-Marcen
In this paper we compute the sum of the -th powers over any finite commutative unital rings, thus generalizing known results for finite fields, the rings of integers modulo …
On power sums of matrices over a finite commutative ring
P. Fortuny, J. M. Grau, A. M. Oller-Marcén +1
In this paper we deal with the problem of computing the sum of the -th powers of all the elements of the matrix ring with and a finite commutative ri…
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…
On the diameter of the commuting graph of the full matrix ring over the real numbers
Jose Maria Grau, Antonio Oller-Marcen, Carmen Tasis
In a recent paper C. Miguel proved that the diameter of the commuting graph of the matrix ring is equal to either if or . But the case $n=…
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,-…