eng Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 2018-09-01 6 1 1 12 10.22044/jas.2017.6012.1301 1251 MAXIMAL PRYM VARIETY AND MAXIMAL MORPHISM M. Farhadi Sangdehi farhadi@du.ac.ir 1 departement of math and computer science Damghan University 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 <br /> 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. http://jas.shahroodut.ac.ir/article_1251_754f567f47608f98c2a43186b7dde0ee.pdf Prym Variety Maximal Curve Maximal Morphism eng Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 2018-09-01 6 1 13 28 10.22044/jas.2017.5482.1278 1252 SIGNED GENERALIZED PETERSEN GRAPH AND ITS CHARACTERISTIC POLYNOMIAL E. Ghasemian e.ghasemian@yahoo.com 1 Gh. H. Fath-Tabar fathtabar@kashanu.ac.ir 2 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran. Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran. Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to<br /> {+, -} 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. http://jas.shahroodut.ac.ir/article_1252_6c32e6bd4ccfe3ab6aa2450e8fa4c181.pdf Singed graph Signed Petersen graph Adjacency matrix Signed Laplacian matrix eng Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 2018-09-01 6 1 29 42 10.22044/jas.2018.5530.1280 1253 IDEALS WITH (d1, . . . , dm)-LINEAR QUOTIENTS L. Sharifan leilasharifan@gmail.com 1 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. 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. http://jas.shahroodut.ac.ir/article_1253_6f8ef72f643795159174715408d317ee.pdf Mapping cone componentwise linear module regularity eng Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 2018-09-01 6 1 43 57 10.22044/jas.2018.6259.1311 1254 ON MAXIMAL IDEALS OF R∞L A. A. Estaji aaestaji@gmail.com 1 A. Mahmoudi Darghadam m.darghadam@yahoo.com 2 Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran. Email: aaestaji@hsu.ac.ir and aaestaji@gmail.com Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran. Email: m.darghadam@yahoo.com Let \$L\$ be a completely regular frame and \$mathcal{R}L\$ be the ring of real-valued continuous functions<br /> on \$L\$.<br /> We consider the set \$\$mathcal{R}_{infty}L = {varphi in mathcal{R} L : uparrow varphi( dfrac{-1}{n}, dfrac{1}{n})<br /> mbox{ is a compact frame for any \$n in mathbb{N}\$}}.\$\$<br /> Suppose that \$C_{infty} (X)\$ is the family of all functions \$f in C(X)\$ for which the<br /> set \${x in X: |f(x)|geq dfrac{1}{n} }\$<br /> is compact, for every \$n in mathbb{N}\$.<br /> Kohls has shown that \$C_{infty} (X)\$ is precisely the intersection<br /> of all the free maximal ideals of \$C^{*}(X)\$.<br /> The aim of this paper is to<br /> extend this result to<br /> the real continuous functions on a<br /> frame and hence we show that \$mathcal{R}_{infty}L\$ is precisely the intersection<br /> of all the free maximal ideals of \$mathcal R^{*}L\$.<br /> This result is used to characterize the maximal ideals in \$mathcal{R}_{infty}L\$. http://jas.shahroodut.ac.ir/article_1254_45a4703f3fc3297b882c27efeed5d7db.pdf Frame Compact Maximal ideal Ring of real valued continuous functions eng Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 2018-09-01 6 1 59 70 10.22044/jas.2018.5360.1273 1255 THE LATTICE OF CONGRUENCES ON A TERNARY SEMIGROUP N. Ashrafi nashrafi@semnan.ac.ir 1 Z. Yazdanmehr zhyazdanmehr@gmail.com 2 Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran. Email: nashrafi@semnan.ac.ir Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran. Email: zhyazdanmehr@gmail.com 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. http://jas.shahroodut.ac.ir/article_1255_585b8d0ca4e05982b434b1a9d2ab912e.pdf Ternary semigroup congruence Lattice eng Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 2018-09-01 6 1 71 80 10.22044/jas.2018.6328.1316 1256 ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS Z. Sepehrizadeh zohreh.sepehri@gmail.com 1 M. R. Rismanchian rismanchian133@gmail.com 2 Department of Pure Mathematics, Shahrekord University , P.O.Box 115, Shahrekord, Iran. Email: zohreh.sepehri@gmail.com Department of Pure Mathematics, Shahrekord University , P.O.Box 115, Shahrekord, Iran. Email: rismanchian133@gmail.com, rismanchian@sku.ac.ir 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. http://jas.shahroodut.ac.ir/article_1256_9cb3d15cf6327aa4481ad9fb54223403.pdf Autocommutativity degree Characteristic degree p-group