فهرست مطالب

Algebraic Structures and Their Applications - Volume:6 Issue:1, 2019
  • Volume:6 Issue:1, 2019
  • تاریخ انتشار: 1397/12/10
  • تعداد عناوین: 8
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  • Saeed Rasouli * Pages 1-21
    The paper is devoted to concern a relationship between rough set theory and universal algebra. Notions of lower and upper rough approximations on an algebraic structure induced by an ideal are introduced and some of their properties are studied. Also, notions of rough subalgebras and rough ideals with respect to an ideal of an algebraic structure, which is an extended notion of subalgebras and ideals in an algebraic structure, are introduced and investigated.
    Keywords: rough set, approximation, universal algebra, subalgebra, rough subalgebra, ideal, rough ideal
  • Mahboobeh Akbarpour, Ghasem Mirhosseinkhani * Pages 23-33
    A category $mathbf{C}$ is called Cartesian closed  provided that it has finite products and for each$mathbf{C}$-object $A$ the functor $(Atimes -): Ara A$ has a right adjoint. It is well known that the category $mathbf{TopFuzz}$  of all topological fuzzes is both complete  and cocomplete, but it is not Cartesian closed. In this paper, we introduce some Cartesian closed subcategories of this category.
    Keywords: Topological fuzz, Exponentiable object, Cartesian closed category
  • Najme Sahami, Majid Mazrooei * Pages 35-45
    In this paper, we employ the concept of the Generalized Discrete Fourier Transform, which in turn relies on the Hasse derivative of polynomials, to give a general construction of Reed-Solomon codes over Galois fields of characteristic not necessarily co-prime with the length of the code. The constructed linear codes  enjoy nice algebraic properties just as the classic one.
    Keywords: Generalized Discrete Fourier Transform, Hasse Derivatives, Linear Codes, Reed-Solomon Codes
  • Dariush Heidari *, Bijan Davvaz Pages 49-56
    In this paper, we introduce a suitable generalization of Cayley graphs that is defined over polygroups (GCP-graph) and give some examples and properties. Then, we mention a generalization of NEPS that contains some known graph operations and apply to GCP-graphs. Finally, we prove that the product of GCP-graphs is again a GCP-graph.
    Keywords: Simple graph, Caylay graph, polygroup, GCP-graph, graph product
  • Azam Kaheni *, Farangis Johari Pages 57-65
    In this paper, groups with trivial intersection between Frattini and derived subgroups are considered. First, some structural properties of these groups are given in an important special case. Then, some family invariants of each $n$-isoclinism family of such groups are stated. In particular, an explicit bound for the order of each center factor group in terms of the order of its derived subgroup is also provided.
    Keywords: Frattini subgroup, Soluble group, Sylow subgroup
  • Marziyeh Beygi, Shohreh Namazi *, Habib Sharif Pages 67-84
    In this article, we shall study the structure of$(a+bu)-$constacyclic codes of arbitrary length over the ring$R=F_{q}+uF_{q}+cdots +u^{e-1}F_{q}$, where $u^{e}=0$, $q$ is apower of a prime number $p$ and $a,b$ are non-zero elements of$F_{q}$. Also we shall find a minimal spanning set for these codes.  %, and completely determine the structure of these codes.For a constacyclic code $C$ we shall determine its minimum Hammingdistance with some properties of $Tor(C)$ as an $a-$constacycliccode over $F_{q}$.
    Keywords: Linear code, constacyclic code, minimal spanning set, minimum Hamming distance
  • Hassan Daghigh *, Ruholla Khodakaramian Gilan Pages 85-99

    In this paper, we propose a new certificateless identification scheme based on isogenies between elliptic curves that is a candidate for quantum-resistant problems.  The proposed scheme has the batch verification property which allows verifying more than one identity by executing only a single challenge-response protocol.

    Keywords: Certificateless Identification Scheme, Elliptic Curves, Isogeny, Cryptography, Pairing
  • Alireza Vahidi * Pages 101-104
    Let $R$ be a commutative Noetherian ring with non-zero identity, $mathfrak{a}$ an ideal of $R$, $M$ a finitely generated $R$--module, and $a_1, ldots, a_n$ an $mathfrak{a}$--filter regular $M$--sequence. The formulabegin{align*}operatorname{H}^i_mathfrak{a}(M)congleft{begin{array}{lll}operatorname{H}^i_{(a_1, ldots, a_n)}(M) & text{for all} mathrm{i< n},\operatorname{H}^{i- n}_mathfrak{a}(operatorname{H}^n_{(a_1, ldots, a_n)}(M)) & text{for all} mathrm{igeq n},end{array}right.end{align*}is known as Nagel-Schenzel formula and is a useful result to express the local cohomology modules in terms of filter regular sequences. In this paper, we provide an elementary proof to this formula.
    Keywords: Filter regular sequences, local cohomology modules, Nagel-Schenzel formula