University of GuilanJournal of Algebra and Related Topics2345-39317220191201Characterization of ^ϕ-amenability and ^ϕ-module amenability of semigroup algebras17407410.22124/jart.2019.14642.1168ENS.Grailo TanhaEsfarayen University of Technology, Esfarayen, North Khorasan,IranJournal Article20191005For every inverse semigroup $S$ with subsemigroup $E$ of idempotents, necessary and sufficient conditions are obtained for the semigroup algebra $\l ^{1}(S)$ to be $\hat{\phi}$-amenable and $\hat{\phi}$-module amenable. Also, we characterize the character amenability of semigroup algebra $l^1(S)$.https://jart.guilan.ac.ir/article_4074_6a8f128b1c1515cb4f46d037c59e761a.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39317220191201Semi n-absorbing ideals in the semiring $\Bbb Z_{0+}$918407610.22124/jart.2020.14003.1157ENJ. N.ChaudhariN. M. UniversityM. D.SuryawanshiDepartment of Mathematics,SSVPS' L. K. Dr. P. R. Ghogrey Science College, Dhule-424 005, India.D. R.BondeDepartment of
Mathematics, ACS College, Dharangaon-425 105, IndiaJournal Article20190801In this paper, all principal (m , n)-closed ideals and principal semi n-absorbing ideals in the semiring of non-negative integers are investigated.https://jart.guilan.ac.ir/article_4076_abb1072e8e07d0693e02a2e8aec33e6b.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39317220191201Connections between graphs and Sheaves1930414010.22124/jart.2020.13887.1154ENP.SagarSwamy Vivekananda Engineering College, Vizianagaram, AP, India0000-0002-4742-8886M.Phani KishoreDepartment of
Information Technology,Gayatri Vidya Parishad College of Engineering (Autonomous), Madhurawada, Visakhapatnam, Andhra Pradesh, India.Journal Article20190717In this paper, we discussed a method to construct a global sheaf space using graphs via Maximal compatibility blocks (MCB's) and we proposed the correspondence between graphs and sheaves. Further we discussed the sheaf constructions for various graphs using MCB's and vice-versa. We also presented some graph theoretical examples for the construction of sheaves.https://jart.guilan.ac.ir/article_4140_14bf2bc5799a3987549caa7de9cc3519.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39317220191201Harary spectrum of generalized composition of graphs and Harary equienergetic graphs3145414110.22124/jart.2020.14263.1161ENH.RamaneDepartment of Mathematics, Karnatak University, Dharwad - 580003, India0000-0003-3122-1669D.PatilDepartment of Mathematics, Karnatak University, Dharwad,IndiaK.AshokaDepartment of Mathematics, Karnatak University, Dharwad - 580003, IndiaB.ParvathaluDepartment of Mathematics, Karnatak University's Karnatak Arts College, Dharwad - 580001, IndiaJournal Article20190829The Harary spectrum of a connected graph $G$ is the collection of the eigenvalues of its Harary matrix. The Harary energy of a graph $G$ is the sum of absolute values of its Harary eigenvalues. Harary equitable partition is defined and is used to obtain Harary spectrum of generalized composition of graphs. Harary equienergetic graphs have been constructed with the help of generalized composition through Harary equitable partition.https://jart.guilan.ac.ir/article_4141_b38a61f4f274ee973786ac502e560b68.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39317220191201The probability that the commutator equation [x,y]=g has solution in a finite group4761414210.22124/jart.2020.15554.1187ENM.HashemiFaculty of mathematical sciences, University of Guilan.M.PirzadehFaculty of Mathematical Sciences, University of GuilanS. A.GorjianUniversity Compos 2, University of GuilanJournal Article20191025Let G be a finite group. For g\in G, an ordered pair $(x_1,y_1)\in G\times G$ is called a solution of the commutator equation $[x,y]=g$ if $[x_1,y_1]=g$.<br /> We consider \rho_g(G)=\{(x,y)| x,y\in G, [x,y]=g\}, then the probability that the commutator equation $[x,y]=g$ has solution in a finite group $G$, written P_g(G), is equal to \frac{|\rho_{g}(G)|}{|G|^2}.<br /> In this paper, we present two methods for the computing P_g(G). First by $GAP, we give certain explicit formulas for P_g(A_n) and P_g(S_n).<br /> Also we note that this method can be applied to any group of small order. Then by using the numerical solutions of the equation xy-zu \equiv t (mod~n), we derive formulas for calculating the probability of $\rho_g(G)$ where $G$ is a two generated group of nilpotency class 2.https://jart.guilan.ac.ir/article_4142_b30a2ba407287566acc0fff8ba3f52db.pdfUniversity of GuilanJournal of Algebra and Related Topics2345-39317220191201Finding a generator matrix of a multidimensional cyclic code6383415910.22124/jart.2020.12926.1142ENR.AndriamifidisoaDepartment of Mathematics and Computer Science, University of Antananarivo, Antananarivo, MadagascarR.LalasoaDepartment of
Mathematics, University
of Antananarivo, Antananarivo, MadagascarT.RabeherimananaDepartment of
Mathematics, University
of Antananarivo, p.O.Box 906,101 Antananarivo, MadagascarJournal Article20190404We generalize Sepasdar's method for finding a gene-<br />\\rator matrix of two-dimensional cyclic codes to find a generating set and a linearly independent subset of a general multicyclic code. From these sets, a basis of the code as a vector subspace can be deduced or constructed. A generator matrix can be then deduced from this basis.https://jart.guilan.ac.ir/article_4159_cb7ac0866eae4244ee47a41c3eb4f8a2.pdf