Algebraic structures and their applications
Year:2017 | Volume:4 | Issue:2|Papers Count:6

In the classical group theory there is an open question: Is every torsion free n-Engel group (for n  4), nilpotent? . To answer the question, Traustason [11] showed that with some additional conditions all 4-Engel groups are locally nilpotent. Here, we gave some partial answer to this question on Engel fuzzy subgroups...

Let 􀀀 be a graph whose each vertex is colored either white or black. If u is a black vertex of 􀀀 such that exactly one neighbor v of u is white, then u changes the color of v to black. A zero forcing set for a graph 􀀀 is a subset of vertices Z  V (􀀀 ) such that if initially the vertices in Z are colored black and the remaining vertices are colored white, then Z changes the color of all vertices in 􀀀 to black. The zero forcing number of 􀀀 is the minimum of jZj over all zero forcing sets for 􀀀 and is denoted by Z(􀀀 )...

The non-commuting graph 􀀀 (G) of a non-abelian group G with the center Z(G) is a graph with the vertex set V (􀀀 (G)) = G\ Z(G) and two distinct vertices x and y are adjacent in 􀀀 (G) if and only if xy≠ yx. The aim of this paper is to compute the spectra of some well-known NC-graphs.

Let R be a commutative Noetherian ring and let M be a  nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the  rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the  rst Ext functors.

In a (t; n)-threshold secret sharing scheme, a secret s is distributed among n participants such that any group of t or more participants can reconstruct the secret together, but no group of fewer than t participants can do. In this paper we propose a veri able (t; n)-threshold multi-secret sharing scheme based on Shao and Cao, and the intractability of the elliptic curve discrete logarithm problem (ECDLP) by using generalized Jacobian of elliptic curves. The proposed scheme has all the bene ts of Shao and Cao, however, our scheme no need to a secure channel. Furthermore, we exploit the techniques via elliptic curves to perform the scheme. This can be very important, because the hardness of discrete logarithm problem on elliptic curves increases security of the proposed scheme.

The aim of this paper is the study of applications of a group in a general fuzzy automaton. For this purpose, we de ne the concepts of fuzzy normal kernel of a general fuzzy automaton, fuzzy kernel of a general fuzzy automaton, adjustable, multiplicative. Then we obtain the relationships between them...