Algebra and Discrete Mathematics, 2019, Vol. 27, № 2http://dspace.nbuv.gov.ua:80/handle/123456789/1504092026-04-20T06:23:02Z2026-04-20T06:23:02ZOn some Leibniz algebras, having small dimensionYashchuk, V.S.http://dspace.nbuv.gov.ua:80/handle/123456789/1884392023-03-01T23:27:38Z2019-01-01T00:00:00ZOn some Leibniz algebras, having small dimension
Yashchuk, V.S.
The first step in the study of all types of algebras is the description of such algebras having small dimensions. The structure of 3-dimensional Leibniz algebras is more complicated than 1 and 2-dimensional cases. In this paper, we consider the structure of Leibniz algebras of dimension 3 over the finite fields. In some cases, the structure of the algebra essentially depends on the characteristic of the field, in others on the solvability of specific equations in the field, and so on.
2019-01-01T00:00:00ZCommutator subgroups of the power subgroups of generalized Hecke groupsKoruoğlu, Ö.Meral, T.Sahin, R.http://dspace.nbuv.gov.ua:80/handle/123456789/1884382023-03-01T23:27:38Z2019-01-01T00:00:00ZCommutator subgroups of the power subgroups of generalized Hecke groups
Koruoğlu, Ö.; Meral, T.; Sahin, R.
Let p, q ≥ 2 be relatively prime integers and let Hp,q be the generalized Hecke group associated to p and q. The generalized Hecke group Hp,q is generated by X(z) = −(z − λp)⁻¹ and Y (z) = −(z + λq)⁻¹ where λp = 2cos π/p and λq = 2 cos π/q.In this paper, for positive integer m, we study the commutator subgroups (Hᵐp,q)′ of the power subgroups Hᵐp,q of generalized Hecke groups Hp,q. We give an application related with the derived series for all triangle groups of the form (0; p, q, n), for distinct primes p, q and for positive integer n.
2019-01-01T00:00:00ZOn the inclusion ideal graph of a posetJahanbakhsh, N.Nikandish, R.Nikmehr, M.J.http://dspace.nbuv.gov.ua:80/handle/123456789/1884372023-03-01T23:27:34Z2019-01-01T00:00:00ZOn the inclusion ideal graph of a poset
Jahanbakhsh, N.; Nikandish, R.; Nikmehr, M.J.
Let (P,≤) be an atomic partially ordered set (poset, briefly) with a minimum element 0 and 𝕿(P) the set of nontrivial ideals of P. The inclusion ideal graph of P, denoted by Ω(P), is an undirected and simple graph with the vertex set 𝕿(P) and two distinct vertices I, J ∈ 𝕿(P) are adjacent in Ω(P) if and only if I ⊂ J or J ⊂ I. We study some connections between the graph theoretic properties of this graph and some algebraic properties of a poset. We prove that Ω(P) is not connected if and only if P = {0, a1, a2}, where a1, a2 are two atoms. Moreover, it is shown that if Ω(P) is connected, then diam(Ω(P)) ≤ 3. Also, we show that if Ω(P) contains a cycle, then girth(Ω(P)) ∈ {3, 6}. Furthermore, all posets based on their diameters and girths of inclusion ideal graphs are characterized. Among other results, all posets whose inclusion ideal graphs are path, cycle and star are characterized.
2019-01-01T00:00:00ZOn the lattice of cyclic codes over finite chain ringsFotue-Tabue, A.Mouaha, C.http://dspace.nbuv.gov.ua:80/handle/123456789/1884362023-03-01T23:27:25Z2019-01-01T00:00:00ZOn the lattice of cyclic codes over finite chain rings
Fotue-Tabue, A.; Mouaha, C.
In this paper, R is a finite chain ring of invariants (q, s), and ℓ is a positive integer fulfilling gcd(ℓ, q) = 1. In the language of q-cyclotomic cosets modulo ℓ, the cyclic codes over R of length ℓ are uniquely decomposed into a direct sum of trace-representable cyclic codes over R and the lattice of cyclic codes over R of length ℓ is investigated.
2019-01-01T00:00:00Z