Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 6 1 2018 09 01 MAXIMAL PRYM VARIETY AND MAXIMAL MORPHISM 1 12 EN M. Farhadi Sangdehi departement of math and computer science Damghan University farhadi@du.ac.ir 10.22044/jas.2017.6012.1301 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. Prym Variety,Maximal Curve,Maximal Morphism http://jas.shahroodut.ac.ir/article_1251.html http://jas.shahroodut.ac.ir/article_1251_754f567f47608f98c2a43186b7dde0ee.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 6 1 2018 09 01 SIGNED GENERALIZED PETERSEN GRAPH AND ITS CHARACTERISTIC POLYNOMIAL 13 28 EN E. Ghasemian Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran. e.ghasemian@yahoo.com Gh. H. Fath-Tabar Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran. fathtabar@kashanu.ac.ir 10.22044/jas.2017.5482.1278 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. Singed graph,Signed Petersen graph,Adjacency matrix,Signed Laplacian matrix http://jas.shahroodut.ac.ir/article_1252.html http://jas.shahroodut.ac.ir/article_1252_6c32e6bd4ccfe3ab6aa2450e8fa4c181.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 6 1 2018 09 01 IDEALS WITH (d1, . . . , dm)-LINEAR QUOTIENTS 29 42 EN L. Sharifan 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. leilasharifan@gmail.com 10.22044/jas.2018.5530.1280 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 http://jas.shahroodut.ac.ir/article_1253.html http://jas.shahroodut.ac.ir/article_1253_6f8ef72f643795159174715408d317ee.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 6 1 2018 09 01 ON MAXIMAL IDEALS OF R∞L 43 57 EN A. A. Estaji 0000-0001-8993-5109 Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran. Email: aaestaji@hsu.ac.ir and aaestaji@gmail.com aaestaji@gmail.com A. Mahmoudi Darghadam Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran. Email: m.darghadam@yahoo.com m.darghadam@yahoo.com 10.22044/jas.2018.6259.1311 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\$. Frame,Compact,Maximal ideal,Ring of real valued continuous functions http://jas.shahroodut.ac.ir/article_1254.html http://jas.shahroodut.ac.ir/article_1254_45a4703f3fc3297b882c27efeed5d7db.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 6 1 2018 09 01 THE LATTICE OF CONGRUENCES ON A TERNARY SEMIGROUP 59 70 EN N. Ashrafi Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran. Email: nashrafi@semnan.ac.ir nashrafi@semnan.ac.ir Z. Yazdanmehr Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran. Email: zhyazdanmehr@gmail.com zhyazdanmehr@gmail.com 10.22044/jas.2018.5360.1273 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 http://jas.shahroodut.ac.ir/article_1255.html http://jas.shahroodut.ac.ir/article_1255_585b8d0ca4e05982b434b1a9d2ab912e.pdf
Shahrood University of Technology Journal of Algebraic Systems 2345-5128 2345-511X 6 1 2018 09 01 ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS 71 80 EN Z. Sepehrizadeh Department of Pure Mathematics, Shahrekord University , P.O.Box 115, Shahrekord, Iran. Email: zohreh.sepehri@gmail.com zohreh.sepehri@gmail.com M. R. Rismanchian Department of Pure Mathematics, Shahrekord University , P.O.Box 115, Shahrekord, Iran. Email: rismanchian133@gmail.com, rismanchian@sku.ac.ir rismanchian133@gmail.com 10.22044/jas.2018.6328.1316 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 http://jas.shahroodut.ac.ir/article_1256.html http://jas.shahroodut.ac.ir/article_1256_9cb3d15cf6327aa4481ad9fb54223403.pdf