Algebraic graphs D(n, q) and their analog graphs D(n,K), where K is a finite commutative ring were used successfully in Coding Theory (as Tanner graphs for the construction of LDPC codes and turbo-codes) and in Cryptography (stream-ciphers, public-keys and tools for the key-exchange protocols. Many properties of cryptography algorithms largely depend on the choice of finite field Fq or commutat...

We exhibit a separable commutative C*-algebra A such that A⊗K is homotopy equivalent to zero, without Mn(A) being so for any n ≥ 1.

Let Ω be a multiply Leibniz isometry equipped with a solvable, analytically natural graph. Recent developments in commutative analysis [5, 16] have raised the question of whether every hyper-partial graph is Noetherian and smoothly Poncelet. We show that

We study D0L power series over commutative semirings. We show that a sequence (cn)n 0 of nonzero elements of a eld A is the coe cient sequence of a D0L power series if and only if there exist a positive integer k and integers i for 1 i k such that cn+k = c 1 n+k 1c 2 n+k 2 : : : c k n for all n 0. As a consequence we solve the equivalence problem of D0L power series over computable elds. TUCS R...

Let R be a commutative ring with identity. Let N and K be two submodules of a multiplication R-module M. Then N=IM and K=JM for some ideals I and J of R. The product of N and K denoted by NK is defined by NK=IJM. In this paper we characterize some particular cases of multiplication modules by using the product of submodules.

Let k be a field, H a cocommutative bialgebra, A a commutative left H-module algebra, Hom(H,A) the k-algebra of the k-linear maps from H to A under the convolution product, Z(H,A) the submonoid of Hom(H,A) whose elements satisfy the cocycle condition and G any subgroup of the monoid Z(H,A). We give necessary and sufficient conditions for the projectivity and flatness over the graded ring of nor...

In [17] Lee and Shiue showed that if R is a non-commutative prime ring, I a nonzero left ideal of R and d is a derivation of R such that [d(x)x, x]k = 0 for all x ∈ I, where k,m, n, r are fixed positive integers, then d = 0 unless R ∼= M2(GF (2)). Later in [1] Argaç and Demir proved the following result: Let R be a non-commutative prime ring, I a nonzero left ideal of R and k,m, n, r fixed posi...

We study connected orientable spacelike hypersurfaces $x:M^{n}rightarrowM_q^{n+1}(c)$, isometrically immersed into the Riemannian or Lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~L_kx=Ax+b$,~ where $L_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $H_{k+1}$ of the hypersurface for a fixed integer $0leq k