Let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $R$.  In this paper we  study the relationship between an$R$-module $M_R$ and the  general polynomial module  $M[x]$ over theskew polynomial ring $R[x;alpha,delta]$. We introduce the notionsof skew-Armendariz modules and skew quasi-Armendariz modules whichare generalizations of $alpha$-Armendariz modules and extend thecla...

A Cayley map is a 2-cell embedding of a Cayley graph into an orientable surface with the same local orientation induced by a cyclic permutation of generators at each vertex. In this paper, we provide classifications of prime-valent regular Cayley maps on abelian groups, dihedral groups and dicyclic groups. Consequently, we show that all prime-valent regular Cayley maps on dihedral groups are ba...

Given a quasi-ordering of labels, a labelled ordered tree s is embedded with gaps in another tree t if there is an injection from the nodes of s into those of t that maps each edge in s to a unique disjoint path in t with greater-or-equivalent labels, and which preserves the order of children. We show that finite trees are well-quasiordered with respect to gap embedding when labels are taken fr...

Throughout this paper, R will denote a commutative ring with identity and M is a unitary R- module and Z will denote the ring of integers. We introduce the graph Ω(M) of module M with the set of vertices contain all nontrivial non-essential submodules of M. We investigate the interplay between graph-theoretic properties of Ω(M) and algebraic properties of M. Also, we assign the values of natura...

A Cayley map is a 2-cell embedding of a Cayley graph into an orientable surface with the same local orientation induced by a cyclic permutation of generators at each vertex. In this paper, we provide classifications of prime-valent regular Cayley maps on abelian groups, dihedral groups and dicyclic groups. Consequently, we show that all prime-valent regular Cayley maps on dihedral groups are ba...

One of the sciences used in digital security systems is cryptography. Cryptography closely related to integer system, especially prime numbers. Prime numbers themselves have been abstracted a lot. form abstraction ideal. Previous studies proven that an Ideal said be ideal on if and only I constructed by element. Other also shown how develops. them research result Dauns, where developed submodul...

A t-(v, k, λ) design is quasi-symmetric if there are only two block intersection sizes. We adapt the Kramer-Mesner construction method for designs with prescribed automorphism groups to the quasi-symmetric case. Using the adapted method, we find many new quasi-symmetric 2-(28, 12, 11) and 2-(36, 16, 12) designs, establish the existence of quasi-symmetric 2-(56, 16, 18) designs, and find three n...

The authors used lexical decision in a dichotic listening situation and measured identity priming across channels to explore whether unattended stimuli can be processed lexically. In 6 experiments, temporal synchronization of prime and target words was manipulated, and acoustic saliency of the unattended prime was varied by embedding it in a carrier sentence or in babble speech. When the prime ...

This paper has two objectives: we first generalize the theory of Abhyankar-Moh to quasi-ordinary polynomials, then we use the notion of approximate roots and that of generalized Newton polygons in order to prove the embedding conjecture for this class of polynomials. This conjecture -made by S.S. Abhyankar and A. Sathayesays that if a hypersurface of the affine space is isomorphic to a coordina...