Journal of Algebra Combinatorics Discrete Structures and Applications (JACODESMATH, Yildiz Technical University - YTU)
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Local System of Simple Locally Finite Associative Algebras
Get PDFAbstract. In this paper, we study local systems of locally finite associative algebras over fields of characteristic p\ge0. We describe the perfect local systems and study the relation between them and their corresponding locally finite associative algebras. 1-perfect and conical local systems are also be considered and described briefl
On the undecidability of Markov properties for Lie superalgebras
Get PDFIn this note, we address an algorithmic problem for Lie superalgebras. As a starting point, we use the Theory of Gröbner-Shirshov bases in order to find a normal form for Higman-Neumann-Neumann-extension (HNN-extension, for short) of Lie superalgebras. Then by using HNN-extension we show that there is no algorithm to determine whether a finitely presented Lie superalgebra satisfies Markov properties
On distance spectra, energies and Wiener index of non-commuting conjugacy class graphs
Get PDFThe non-commuting conjugacy class graph (abbreviated as NCCC-graph) of a finite non-abelian group is a simple undirected graph whose vertex set is the set of conjugacy classes of non-central elements of and two vertices, and are adjacent if for all and . In this paper, we compute distance spectrum, distance Laplacian spectrum, distance signless Laplacian spectrum along with their respective energies and Wiener index of NCCC-graphs of when the central quotient of is isomorphic to (for any prime ) or (for any integer ). As a consequence, we compute various distance spectra, energies and Wiener index of NCCC-graphs of the dihedral group, dicyclic group, semidihedral group along with the groups , and . Thus we obtain sequences of positive integers that can be realized as Wiener index of NCCC-graphs of certain groups. In particular, we solve Inverse Wiener index Problem for NCCC-graphs of groups when is a perfect square. We further characterize the above-mentioned groups such that their NCCC-graphs are D-integral, DL-integral and DQ-integral. We also compare various distance energies of NCCC-graphs of the above mentioned groups and characterize those groups subject to the inequalities involving various distance energies
An algorithm for counting domino tilings of a rectangular chessboard
Get PDFA recursive method is developed for counting domino tilings of a rectangular chessboard (the dimer problem). Based on this method, a new and enhanced recursive algorithm is proposed for solving this problem. Close connections with Fibonacci numbers are traced out
On additive cyclic codes over F_4+uF_4
Get PDFThis article studies additive cyclic codes over R = F4 + uF4, where u^2 = 0. We obtain generator polynomials for these codes and provide necessaryand sufficient conditions for additive codes to be self-orthogonal and self-dual codes over R with respect to the symplectic inner product. Additive self-orthogonal codes over F4 with respect to the symplectic inner product are used to construct quantum codes. We demonstrate that the Gray image of additive self-orthogonal codes over R results in additive self-orthogonal codes over F4. Additionally, we prove that binary self-orthogonal codes can be obtained from additive self-orthogonal codes over R with respect to the symplectic inner product
Local and 2-local 1/2-derivation on naturally graded non-Lie p-filiform algebras
No full textThis paper is devoted to study local and 2-local 1/2-derivation on p-filiform Leibniz algebras. We prove that p-filiform Leibniz algebras as a rule admit local(2-local) 1/2-derivations which are not 1/2-derivations
On strongly semicommutative modules
Get PDFFor a left module over a non-commutative ring , we define the concept of a strongly semicommutative module as a generalization of the reduced module. This notion constitutes a distinct and stronger category within the class of semicommutative modules. We demonstrate that a module is strongly semicommutative if and only if is strongly semicommutative. Additionally, we establish that is strongly semicommutative if and only if is strongly semicommutative; this is also equivalent to being strongly semicommutative. Among our findings, we prove that if is strongly semicommutative, then for any reduced submodule of , the quotient module is also strongly semicommutative. We provide examples of semicommutative modules that are not strongly semicommutative and show that the class of strongly semicommutative modules remains closed under localization
Good codes from twisted group algebras
Get PDFIn this paper, we shall give an explicit proof that constacyclic codes over finite commutative rings can be realized as ideals in some twisted group rings. Also, we shall study isometries between those codes and, finally, we shall study k-Galois LCD constacyclic codes over finite fields. In particular, we shall characterize constacyclic LCD codes with respect to Euclidean inner product in terms of its idempotent generators and the classical involution using the twisted group algebras structures and find some good LCD code
A supercharacter theory for PSL(2,q) and SO(3,q)
Get PDFThe concept of a supercharacter theory for a finite group was introduced in 2008 by Diaconis and Iasaacs in [6]. In their article the notion of irreducible characters and conjugacy classes is generalized to superchacters and superclasses while still maintaining important information about the group. This article continues an investigation of a specific supercharacter theory where the supercharacters are taken to be sums of irreducible characters of the same degree. We show this supercharacter theory construction can be done for all projective special linear groups PSL(2,q) and all special orthogonal groups SO(3,q) where q is any power of an (even or odd) prime
Minimum distance bounds for linear codes over GF(11)
Get PDFLet code be a linear code of length , dimension and minimum Hamming distance over . One of the most important problems in coding theory is to construct codes with best possible minimum distances. In this paper 36 new cyclic and quasi-cyclic (QC) codes over GF(11) are presented and the table from [4] is enlarged by adding three new dimensions