We present some observations on a restricted variant of unitary Cayley graphs modulo n, and implications for a decomposition of elements of symplectic operators over the integers modulo n. We define quadratic unitary Cayley graphs Gn, whose vertex set is the ring Zn, and where residues a, b modulo n are adjacent if and only if their difference is a quadratic residue. By bounding the diameter of...

Let α be a prime Hurwitz integer. Hα, which is the set of residual class with respect to related modulo function in rings integers, subset H, all integers. We consider left congruent and, domain related
 this study ZN(α), ring ordinary integers N(α) elements, norm integer α. In study, we present an algebraic construction technique, formed depending on
 two operations, for codes over T...

Let m,n > 1 be integers and Pn,m be the point set of the projective (n − 1)-space (defined by [2]) over the ring Zmof integers modulo m. Let An,m = (auv) be the matrix with rows and columns being labeled by Pn,m, where auv = 1 if the inner product 〈u, v〉 = 0 and auv = 0 otherwise. Let Bn,m = An,mA t n,m. The eigenvalues of Bn,m have been studied by [1, 2, 3], where their applications in the stu...

Let $R=k[x_1,x_2,cdots, x_N]$ be a polynomial ring over a field $k$. We prove that for any positive integers $m, n$, $text{reg}(I^mJ^nK)leq mtext{reg}(I)+ntext{reg}(J)+text{reg}(K)$ if $I, J, Ksubseteq R$ are three monomial complete intersections ($I$, $J$, $K$ are not necessarily proper ideals of the polynomial ring $R$), and $I, J$ are of the form $(x_{i_1}^{a_1}, x_{i_2}^{a_2}, cdots, x_{i_l...