فهرست مطالب

Algebraic Systems - Volume:6 Issue: 1, Summer - Autumn 2018

Journal of Algebraic Systems
Volume:6 Issue: 1, Summer - Autumn 2018

  • تاریخ انتشار: 1397/04/28
  • تعداد عناوین: 6
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  • M. Farhadi Sangdehi * Pages 1-12
    We investigated maximal Prym varieties on finite fields by attaining their upper bounds on the number of rational points. This concept gave us a motivation for defining a generalized definition of maximal curves i.e. maximal morphisms. By MAGMA, we give some non-trivial examples of maximal morphisms that results in non-trivial examples of maximal Prym varieties.
    Keywords: Prym Variety, Maximal Curve, Maximal Morphism
  • E. Ghasemian, Gh. H. Fath-Tabar * Pages 13-28
    Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to {, -} is the sign function on E(G). In this paper, we obtain k-th signed spectral moment and k-th signed Laplacian spectral moment of Gs together with coefficients of their signed characteristic polynomial and signed Laplacian characteristic polynomial are calculated.
    Keywords: Singed graph, Signed Petersen graph, Adjacency matrix, Signed Laplacian matrix
  • L. Sharifan * Pages 29-42
    In this paper, we introduce the class of ideals with $(d_1,\ldots,d_m)$-linear quotients generalizing the class of ideals with linear quotients. Under suitable conditions we control the numerical invariants of a minimal free resolution of ideals with $(d_1,\ldots,d_m)$-linear quotients. In particular we show that their first module of syzygies is a componentwise linear module.
    Keywords: Mapping cone, componentwise linear module, regularity
  • A. A. Estaji *, A. Mahmoudi Darghadam Pages 43-57
    Let $L$ be a completely regular frame and $\mathcal{R}L$ be the ring of real-valued continuous functions on $L$.
    We consider the set $$\mathcal{R}_{\infty}L = \{\varphi \in \mathcal{R} L : \uparrow \varphi( \dfrac{-1}{n}, \dfrac{1}{n}) \mbox{ is a compact frame for any $n \in \mathbb{N}$}\}.$$ Suppose that $C_{\infty} (X)$ is the family of all functions $f \in C(X)$ for which the set $\{x \in X: |f(x)|\geq \dfrac{1}{n} \}$ is compact, for every $n \in \mathbb{N}$.
    Kohls has shown that $C_{\infty} (X)$ is precisely the intersection of all the free maximal ideals of $C^{*}(X)$.
    The aim of this paper is to extend this result to the real continuous functions on a frame and hence we show that $\mathcal{R}_{\infty}L$ is precisely the intersection of all the free maximal ideals of $\mathcal R^{*}L$.
    This result is used to characterize the maximal ideals in $\mathcal{R}_{\infty}L$.
    Keywords: Frame, Compact, Maximal ideal, Ring of real valued continuous functions
  • N. Ashrafi *, Z. Yazdanmehr Pages 59-70
    In this paper we investigate some properties of congruences on ternary semigroups. We also define the notion of congruence on a ternary semigroup generated by a relation and we determine the method of obtaining a congruence on a ternary semigroup T from a relation R on T. Furthermore we study the lattice of congruences on a ternary semigroup and we show that this lattice is not generally modular, it is not even semimodular. Then we indicate some conditions under which this lattice is modular.
    Keywords: Ternary semigroup, congruence, lattice
  • Z. Sepehrizadeh, M. R. Rismanchian * Pages 71-80
    In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic in G. We determine the upper and lower bounds for this probability. We also obtain a special lower bound, when H is a cyclic p-subgroup of G.
    Keywords: Autocommutativity degree, Characteristic degree, p-group