JAS Shahrood University of Technology Journal of Algebraic Systems 2345-5128 Shahrood University of Technology 4 10.22044/jas.2017.6012.1301 Original Manuscript MAXIMAL PRYM VARIETY AND MAXIMAL MORPHISM MAXIMAL PRYM VARIETY AND MAXIMAL MORPHISM Farhadi Sangdehi M. departement of math and computer science Damghan University 01 09 2018 6 1 1 12 17 07 2017 15 11 2017 Copyright © 2018, Shahrood University of Technology. 2018 http://jas.shahroodut.ac.ir/article_1251.html

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.

Prym Variety Maximal Curve Maximal Morphism
JAS Shahrood University of Technology Journal of Algebraic Systems 2345-5128 Shahrood University of Technology 4 10.22044/jas.2017.5482.1278 Original Manuscript SIGNED GENERALIZED PETERSEN GRAPH AND ITS CHARACTERISTIC POLYNOMIAL Signed generalized Petersen graph and its characteristic polynomial Ghasemian E. Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran. Fath-Tabar Gh. H. Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran. 01 09 2018 6 1 13 28 04 03 2017 01 12 2017 Copyright © 2018, Shahrood University of Technology. 2018 http://jas.shahroodut.ac.ir/article_1252.html

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.

Singed graph Signed Petersen graph Adjacency matrix Signed Laplacian matrix
JAS Shahrood University of Technology Journal of Algebraic Systems 2345-5128 Shahrood University of Technology 4 10.22044/jas.2018.5530.1280 Original Manuscript IDEALS WITH (d1, . . . , dm)-LINEAR QUOTIENTS Ideals with (d_1,...,d_m)-linear quotients Sharifan L. Department of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran and School of Mathematics, Institute for research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran. 01 09 2018 6 1 29 42 17 03 2017 08 01 2018 Copyright © 2018, Shahrood University of Technology. 2018 http://jas.shahroodut.ac.ir/article_1253.html

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.

Mapping cone componentwise linear module regularity
JAS Shahrood University of Technology Journal of Algebraic Systems 2345-5128 Shahrood University of Technology 4 10.22044/jas.2018.6259.1311 Original Manuscript

ON MAXIMAL IDEALS OF RL

On maximal ideals of \$mathcal{R}_{infty}L\$
Estaji A. A. Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran. Email: aaestaji@hsu.ac.ir and aaestaji@gmail.com Mahmoudi Darghadam A. Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran. Email: m.darghadam@yahoo.com 01 09 2018 6 1 43 57 26 09 2017 12 01 2018 Copyright © 2018, Shahrood University of Technology. 2018 http://jas.shahroodut.ac.ir/article_1254.html

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\$.

Frame Compact Maximal ideal Ring of real valued continuous functions
JAS Shahrood University of Technology Journal of Algebraic Systems 2345-5128 Shahrood University of Technology 4 10.22044/jas.2018.5360.1273 Original Manuscript THE LATTICE OF CONGRUENCES ON A TERNARY SEMIGROUP THE LATTICE OF CONGRUENCES ON A TERNARY SEMIGROUP Ashrafi N. Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran. Email: nashrafi@semnan.ac.ir Yazdanmehr Z. Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran. Email: zhyazdanmehr@gmail.com 01 09 2018 6 1 59 70 29 01 2017 26 01 2018 Copyright © 2018, Shahrood University of Technology. 2018 http://jas.shahroodut.ac.ir/article_1255.html

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.

Ternary semigroup congruence Lattice
JAS Shahrood University of Technology Journal of Algebraic Systems 2345-5128 Shahrood University of Technology 4 10.22044/jas.2018.6328.1316 Original Manuscript ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS On the characteristic degree of finite groups Sepehrizadeh Z. Department of Pure Mathematics, Shahrekord University , P.O.Box 115, Shahrekord, Iran. Email: zohreh.sepehri@gmail.com Rismanchian M. R. Department of Pure Mathematics, Shahrekord University , P.O.Box 115, Shahrekord, Iran. Email: rismanchian133@gmail.com, rismanchian@sku.ac.ir 01 09 2018 6 1 71 80 23 10 2017 04 03 2018 Copyright © 2018, Shahrood University of Technology. 2018 http://jas.shahroodut.ac.ir/article_1256.html

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.

Autocommutativity degree Characteristic degree p-group